Frank solutions for Mathematics [English] Class 9 ICSE chapter 8 - Simultaneous Linear Equations [Latest edition]

Solve the following simultaneous equations by the substitution method:
2x + y = 8
3y = 3 + 4x

Solve the following simultaneous equations by the substitution method:
x + 3y= 5
7x - 8y = 6

Solve the following simultaneous equations by the substitution method:
5x + 4y - 23 = 0
x + 9 = 6y

Solve the following simultaneous equations by the substitution method:
2x + 3y = 31
5x - 4 = 3y

Solve the following simultaneous equations by the substitution method:
7x - 3y = 31
9x - 5y = 41

Solve the following simultaneous equations by the substitution method:
13 + 2y = 9x
3y = 7x

Solve the following simultaneous equations by the substitution method:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5

Solve the following simultaneous equations by the substitution method:
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8

Solve the following simultaneous equations by the substitution method:
3 - (x + 5) = y + 2
2(x + y) = 10 + 2y

Solve the following simultaneous equations by the substitution method:
7(y + 3) - 2(x + 2) = 14
4(y - 2) + 3(x - 3) = 2

Solve the following simultaneous equations :
6x + 3y = 7xy
3x + 9y = 11xy

Solve the following simultaneous equation :
8v - 3u = 5uv
6v - 5u = -2uv

Solve the following simultaneous equations :
3(2u + v) = 7uv
3(u + 3v) = 11uv

Solve the following simultaneous equations :
2(3u - v) = 5uv
2(u + 3v) = 5uv

Solve the following simultaneous equations:
13a - 11b = 70
11a - 13b = 74

Solve the following simultaneous equations:
41x + 53y = 135
53x + 41y = 147

Solve the following simultaneous equations:
65x - 33y = 97
33x - 65y = 1

Solve the following simultaneous equations:
103a + 51b = 617
97a + 49b = 583

Solve the following pairs of equations:

`(3)/(5) x - (2)/(3) y + 1` = 0

`(1)/(3) y + (2)/(5) x ` = 4

Solve the following pairs of equations:

`x/(3) + y/(4)` = 11

`(5x)/(6) - y/(3)` = -7

Solve the following pairs of equations:

`(3)/(2x) + (2)/(3y)` = 5

`(5)/x - (3)/y` = 1

Solve the following pairs of equations:

`(3)/x - (1)/y` = -9

`(2)/x + (3)/y` = 5

Solve the following pairs of equations:
y - x = 0.8

`(13)/(2(x + y)) = 1`

Solve the following pairs of equations:

`(2)/x + (3)/y = (9)/(xy)`

`(4)/x + (9)/y = (21)/(xy)`
Where x ≠ 0, y ≠ 0

Solve the following pairs of equations:

`(x + y)/(xy)` = 2

`(x - y)/(xy)` = 6

Solve the following pairs of equations:

`(2)/(x + 1) - (1)/(y - 1) = (1)/(2)`

`(1)/(x + 1) + (2)/(y - 1) = (5)/(2)`

Solve the following pairs of equations:

`(6)/(x + y) = (7)/(x - y) + 3`

`(1)/(2(x + y)) = (1)/(3( x - y)`
Where x + y ≠ 0 and x - y ≠ 0

Solve the following pairs of equations:

`(5)/(x + y) - (2)/(x - y)` = -1

`(15)/(x + y) + (7)/(x - y)` = 10.

Solve the following pairs of equations:

`(2)/(3x + 2y) + (3)/(3x - 2y) = (17)/(5)`

`(5)/(3x + 2y) + (1)/(3x - 2y)` = 2

Solve the following pairs of equations:

`(xy)/(x + y) = (6)/(5)`

`(xy)/(y - x)` = 6
Where x + y ≠ 0 and y - x ≠ 0

If 2x + y = 23 and 4x - y = 19 :  find the value of x - 3y and 5y - 2x.

If 10y = 7x - 4 and 12x + 18y = 1 ; find the value of 4x + 6y and 8y - x.

`4x + 6/y = 15 and 6x - 8/y = 14.` Hence, find a if y = ax - 2.

`(3)/x - (2)/y` = 0 and `(2)/x + (5)/y` = 19, Hence, find a if y = ax + 3.

Can the following equations hold simultaneously?
7y - 3x = 7
5y - 11x = 87
5x + 4y = 43
If yes, find the value of x and y.

If the following three equations hold simultaneously for x and y, find the value of 'm'.
2x + 3y + 6 = 0
4x - 3y - 8 = 0
x + my - 1 = 0

Draw the graphs of the following linear equations:
x = 3

Draw the graphs of the following linear equations:
y + 5 = 0

Draw the graphs of the following linear equations:
3x + 2y - 6 = 0

Draw the graphs of the following linear equations:
5x - 5y = 8

Draw the graph for each of the following equation: Also, find the coordinates of the points where the graph of the equation meets the coordinate axes:
`(1)/(2) x + (1)/(3) y` = 1

Draw the graph for each of the following equation: Also, find the coordinates of the points where the graph of the equation meets the coordinate axes:

`(3x + 14)/(2) = (y - 10)/(5)`

Draw the graph of the equation 4x - 3y + 12 = 0.
Also, find the area of the triangle formed by the line drawn and the coordinate axes.

Draw the graph of the equation
y = 5x - 4 Find graphically
a. the value of x, when y = 1
b. the value of y, when x = -2

Use the given table and draw the graph of a straight line.

Find graphically the values of 'p' and 'q'.

A straight line passes through the points (2, 5) and (-4, -7). Plot these points on a graph paper and draw the straight line passes through these points. If points (a, -1) and (-5, b) lie on the line drawn, find the value of a and b.

Solve the following equations graphically :
x + 3y = 8
3x = 2 + 2y

Solve the following equations graphically :
2x + 4y = 7
3x + 8y = 10

Solve the following equations graphically :
2x - y = 9
5x + 2y = 27

Solve the following equations graphically :
x + 4y + 9 = 0
3y = 5x - 1

Solve the following equations graphically :
x = 4

`(3x)/(3) - y = 5`

Solve the following equations graphically :
3y = 5 - x
2x = y + 3

Solve the following equations graphically :
x - 2y = 2

`x/(2) - y` = 1

Solve the following equations graphically :
2x - 6y + 10 = 0
3x - 9y + 25 = 0

Solve the following equations graphically :

`2 + (3y)/x = (6)/x`

`(6x)/y - 5 = (4)/y`

Solve the following equations graphically :
x+ 2y - 7 = 0
2x - y - 4 = 0

Find graphically the vertices of the triangle, whose sides have the equations 2y - x = 8, 5y -x = 14 and y = 2x - 1.

Find graphically the vertices of the triangle, whose sides are given by 3y = x + 18, x + 7y = 22 and y + 3x = 26.

Solve the following system of linear equations graphically :
4x - 5y - 20 = 0
3x + 3y - 15 = 0
Determine the vertices of the triangle formed by the lines, represented by the above equations and the y-axis.

Solve the following system of equations graphically
x - y + 1 = 0
4x + 3y = 24

Draw the graph of the following equations :
3x + 2y + 6 = 0
3x + 8y - 12 = 0
Also, determine the co-ordinates of the vertices of the triangle formed by these lines and x-axis.

Solve the following system of equations graphically:
2x = 23 - 3y
5x = 20 + 8y
Also, find the area of the triangle formed by these lines and x-axis in each graph.

Solve the following system of equations graphically:
6x - 3y + 2 = 7x + 1
5x + 1 = 4x - y + 2
Also, find the area of the triangle formed by these lines and x-axis in each graph.

The length of a rectangle is twice its width. If its perimeter is 30 units, find its dimensions.

The difference of two numbers is 3, and the sum of three times the larger one and twice the smaller one is 19. Find the two numbers.

If a number is thrice the other and their sum is 68, find the numbers.

The sum of four times the first number and three times the second number is 15. The difference of three times the first number and twice the second number is 7. Find the numbers.

In a two-digit number, the sum of the digits is 7. The difference of the number obtained by reversing the digits and the number itself is 9. Find the number.

The sum of a two-digit number and the number obtained by reversing the digits is 110 and the difference of two digits is 2. Find the number.

Seven more than a 2-digit number is equal to two less than the number obtained by reversing the digits. The sum of the digits is 5. Find the number.

If 2 is added to the numerator and denominator it becomes `(9)/(10)` and if 3 is subtracted from the numerator and denominator it becomes `(4)/(5) `Find the fraction.

The ratio of two numbers is `(2)/(5)`. If 4 is added in first and 32 is subtracted from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes `(1)/(2)`. Find the fraction.

If 1 is added to the denominator of a fraction, the fraction becomes `(1)/(2)`. If 1 is added to the numerator of the fraction, the fraction becomes 1. Find the fraction.

The age of the father is seven times the age of the son. Ten years later, the age of the father will be thrice the age of the son. Find their present ages.

The present ages of Kapil and Karuna are in the ratio 2 : 3. Six years later, the ratio will be 5 : 7. Find their present ages.

A father's age is three times the age of his child. After 12 years, twice the age of father will be 36 more than thrice the age of his child. Find his present age.
* Question modified

In a triangle, the sum of two angles is equal to the third angle. If the difference between these two angles is 20°, determine all the angles.

In a ABC, ∠A = x°, ∠B = (2x - 30)°, ∠C = y° and also, ∠A + ∠B = one right angle. Find the angles. Also, state the type of this triangle.

A two-digit number is such that the ten's digit exceeds thrice the unit's digit by 3 and the number obtained by interchanging the digits is 2 more than twice the sum of the digits. Find the number.

Anil and Sunita have incomes in the ratio 3 : 5. If they spend in the ratio 1 : 3, each saves T 5000. Find the income of each.

The ratio of passed and failed students in an examination was 3 : 1. Had 30 less appeared and 10 less failed, the ratio of passes to failures would have been 13 : 4. Find the number of students who appeared for the examination.

An eraser costs Rs. 1.50 less than a sharpener. Also, the cost of 4 erasers and 3 sharpeners is Rs.29. Taking x and y as the costs (in Rs.) of an eraser and a sharpener respectively, write two equations for the above statements and find the value of x and y.

A person goes 8 km downstream in 40 minutes and returns in 1 hour. Determine the speed of the person in still water and the speed of the stream.

A boat goes 18 km upstream in 3 hours and 24 km downstream in 2 hours. Find the speed of the boat in still water and the speed of the stream.

Salman and Kirti start at the same time from two places 28 km apart. If they walk in the same direction, Salman overtakes Kirti in 28 hours but if they walk in the opposite directions, they meet in 4 hours. Find their speeds (in km/h).

A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol. How much of each solution should be used?

9 pens and 5 pencils cost Rs.32, and 7 pens and 8 pencils cost Rs.29. Find the unit price for each pen and pencil.

Sunil and Kafeel both have some oranges. If Sunil gives 2 oranges to Kafeel, then Kafeel will have thrice as many as Sunil. And if Kafeel gives 2 oranges to Sunil, then they will have the same numbers of oranges. How many oranges does each have?

Samidha and Shreya have pocket money Rs.x and Rs.y respectively at the beginning of a week. They both spend money throughout the week. At the end of the week, Samidha spends Rs.500 and is left with as much money as Shreya had in the beginning of the week. Shreya spends Rs.500 and is left with `(3)/(5)` of what Samidha had in the beginning of the week. Find their pocket money.

Two mobiles S1 and S2 are sold for Rs. 10,490 making 4% profit on S1 and 6% on S2. If the two mobiles are sold for Rs.10,510, a profit of 6% is made on S1 and 4% on S2. Find the cost price of both the mobiles.

A and B can build a wall in `6(2)/(3)` days. If A's one day work is `1(1)/(4)` of one day work of B, find in 4 how many days A and B alone can build the wall.