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5x - 7y = 12

x – 4y = 5

From the

5x - 7y = 12 equation 1

x – 4y = 5 equation 2

This system of equation can be solved using

From equation 2 we get x = 4 y + 5

Substitute x in Eq 1 5 * ( 4y+ 5 ) – 7 y = 12

20y – 7y = 12 – 25

So y = -1

Now we plug in y to get x

x = 4y + 5 = 4 (-1) + 5 = 1

x = 1 ; y = -1

4x – 2 y = 6 equation 1

3x + 4y = 10 equation 2

This system of equation can be solved using

In the first step we do equation 1 times 3

12x – 6 y = 18

In the second step we do equation 2 times 4

12x + 16 y = 40

On subtracting we get - 22y = -22

y =1.

We plug in y to find x so x = 2

x = 2 ; y = 1