Advertisements
Advertisements
Question
Solve for x and y:
7(y + 3) – 2(x + 2) = 14, 4(y – 2) + 3(x – 3) = 2
Solution
The given equations are:
7(y + 3) – 2(x + 2) = 14
⇒ 7y + 21 – 2x – 4 = 14
⇒-2x + 7y = -3 ……..(i)
and 4(y – 2) + 3(x – 3) = 2
⇒4y – 8 + 3x – 9 = 2
⇒3x + 4y = 19 ……….(ii)
On multiplying (i) by 4 and (ii) by 7, we get:
-8x + 28y = -12 ……(iii)
21x + 28y = 133 ……(iv)
On subtracting (iii) from (iv), we get:
29x = 145
⇒x = 5
On substituting x = 5 in (i), we get:
-10 + 7y = -3
⇒7y = (-3 + 10) = 7
⇒y = 1
Hence, the solution is x = 5 and y = 1.
APPEARS IN
RELATED QUESTIONS
The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 3 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
In the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:
x - 2y - 8 = 0
5x - 10y - 10 = 0
For what value of k, the following system of equations will represent the coincident lines?
x + 2y + 7 = 0
2x + ky + 14 = 0
Solve for x and y:
x – y = 3, `x/3 + y/2` = 6
Find the values of a and b for which the system of linear equations has an infinite number of solutions:
2x + 3y = 7, 2ax + (a + b)y = 28.
A number consists of two digits. When it is divided by the sum of its digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. Find the number.
If 2 is added to the numerator of a fraction, it reduces to `(1/2) `and if 1 is subtracted from the denominator, it reduces to `(1/3)`. Find the fraction.
In a cyclic quadrilateral ABCD, it is given ∠A = (2x + 4)°, ∠B = (y + 3)°, ∠C = (2y + 10)° and ∠D = (4x – 5)°. Find the four angles.
The sum of two numbers is 80. The larger number exceeds four times the smaller one by 5. Find the numbers.
A pair of linear equations which has a unique solution x = 2, y = –3 is ______.
