Advertisements
Advertisements
Question
If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form ______.
Options
y – x = 0
x + y = 0
–2x + y = 0
–x + 2y = 0
Solution
If a linear equation has solutions (–2, 2), (0, 0) and (2, –2), then it is of the form x + y = 0.
Explanation:
Let us consider a linear equation ax + by + c = 0 ...(i)
Since, (–2, 2), (0, 0) and (2, –2) are the solutions of linear equation therefore it satisfies the equation (i), we get
At point (–2, 2), –2a + 2b + c = 0 ...(ii)
At point (0, 0), 0 + 0 + c = 0 ⇒ c = 0 ...(iii)
And at point (2, –2), 2a – 2b + c = 0 ...(iv)
From equations (ii) and (iii),
c = 0 and –2a + 2b + 0 = 0,
–2a = –2b,
`a = (2b)/2`
⇒ a = b
On putting a = b and c = 0 in equation (i),
bx + by + 0 = 0
⇒ bx + by = 0
⇒ –b(x + y) = 0
⇒ x + y = 0, b ≠ 0
Hence, x + y = 0 is the required form of the linear equation.
APPEARS IN
RELATED QUESTIONS
Write four solutions for the following equation:
2x + y = 7
Check whether the following is the solution of the equation x – 2y = 4 or not:
(0, 2)
Check whether the following is the solution of the equation x – 2y = 4 or not:
(1, 1)
Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation :
5x – 2y = 10
The sum of a two digit number and the number obtained by reversing the order of its digits
is 121. If units and ten’s digit of the number are x and y respectively then write the linear
equation representing the above statement.
Any point on the line y = x is of the form ______.
The coordinates of points in the table:
| x | 0 | 1 | 2 | 3 | 4 |
| y | 2 | 3 | 4 | –5 | 6 |
represent some of the solutions of the equation x – y + 2 = 0.
The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation
`C = (5F - 160)/9`
- If the temperature is 86°F, what is the temperature in Celsius?
- If the temperature is 35°C, what is the temperature in Fahrenheit?
- If the temperature is 0°C what is the temperature in Fahrenheit and if the temperature is 0°F, what is the temperature in Celsius?
- What is the numerical value of the temperature which is same in both the scales?
The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = `(5F - 160)/9`. What is the numerical value of the temperature which is same in both the scales?
If the temperature of a liquid can be measured in Kelvin units as x°K or in Fahrenheit units as y°F, the relation between the two systems of measurement of temperature is given by the linear equation `y = 9/5 (x - 273) + 32`. If the temperature is 158°F, then find the temperature in Kelvin.
