(1) x=4y+3

2x+5y=-7

rewrite as

x-4y=3

2x+5y=-7

multiply the first equation by 2 to get

2x-8y=6 and now write the second

2x+5y=-7

Subtract the second equation from the first to get

-13y=13or that y=-1

substituting this in, say, x-4y=3 we get x-4(-1)=3

or x=-1

Verify as -1+4=3 or as 2(-1)+5(-1)=-2-5=-7

(2) x=-2/3y+3/4

12x+8y=6

rewrite as

x+2/3y=3/4

12x+8y=6

Multiply the first equation by 12 to get

12x+8y=9

It is not possible for 12x+8y=6 and 12x+8y=9 at the same time.

These equations are of two parallel lines with no points in common. There are no solutions.

(3)y=5x+2

y=9x-6

These two equations give that 5x+2=9x-6 since both are equal to y

subtract 5x from both sides to get 2=4x-6, add 6 to both sides to get

8=4x or that x=2. Substituting in either equation say the first y=5(2)+2=12

or the second y=9(2)-6=12

(4)2x-y=-15

5x+6y=5

Rewrite to align the equations as

2x -y=-15

5x+6y=5

Multiply the first equation by 6 to get

12x-6y=-90 the second written below is

5x+6y=5

Add to get

17x=-85 or that x=-5

Substitute in the first equation to get

2(-5)-y=-15 which gives -10-y=-15 or that -y=-5 or y=5

The second equation can be used to verify this result as 5(-5)+6(5)=5