Question

Find the solution set of the following linear equations: 2x − 5y + 4 = 0, 2x + y – 8 = 0
(a) x = 3, y = 2
(b) x = 3, y = 4
(c) x = 1, y = 2
(d) x = 1, y = 3

Answer 1

Hint: Since the coefficient of x is the same in both terms , eliminate x by subtracting one equation from another, now solve for y and after getting put this y in either of 1st or 2nd equation to get x.

Complete step-by-step answer:

In this question, we are given two linear equations: 2x − 5y + 4 = 0, 2x + y – 8 = 0
We need to find the solution set (values of x and y) for this pair of linear equations.
2x − 5y + 4 = 0 …(1)
2x + y – 8 = 0 …(2)
To solve this pair of linear equations, we will first subtract equation (1) from equation (2).
$2x+y-2x+5y=8+4$
$6y=12$
Dividing both sides by 6, we will get the following:
$y=2$
Now, we will substitute this value of y to equation (2)
2x + y – 8 = 0
2x + 2 – 8 = 0
2x = 6
So, x = 3
Hence, we have x = 3 and y = 2.
This is our final answer.
Hence, option (a) is correct.

Note: We can also solve this question by doing the following:
Rewrite equation (2) as y = 8 – 2x. Substitute this in equation (1).
2x – 5(8-2x) + 4 = 0
Solve this to find x = 3. Now, substitute this to y = 8 – 2x which we found earlier. Solve this to find y = 2. This is the final answer.