Question

Solve :

5x - 7y = 12

5y - 2x = - 7

Answer 1

5x - 7y = 12
5y - 2x = -7
5x - 7y = 12
-2x + 5y = -7
3x + 2y = 5
3(2) + 2(-1) = 5
6 + (-1) = 5
6 - 1 = 5
5 = 5

Answer 2

there is one solution:

use elimination method

5x - 7y = 12
5y - 2x = -7 ---> change equation around

5x - 7y = 12
-2x + 5y = -7

2 x ( 5x - 7y) = 2 x (12) multiply both sides by 2
5 x (-2x +5y) = 5 x (-7)

this give you
10x - 14y =24
-10x+25y = -35 add down
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11y = - 11 x is eliminated to find y value

y = -1 input to one of the original equations

5(-1) - 2x = -7

-5 - 2x = -7
+5 +5 add 5 to both sides
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-2x = -2
x = 1

your coordinates for when they intersect is at (1, -1)
one solution