Which expression gives the x-coordinate of the solution of the system?

{2x + 3y = 5

{3x + 5y = 7

(it's one big bracket.)

Which expression gives the y-coordinate of the solution of the system?

{2x + y = 2

{3x + 4y = - 22

and

Which expression shows the solution of the system?

{5x + 4y = 2

{-2y = 8 + 4x

1) the x-coordinate of the system can be given as follow:

2x+3y = 5 (i)

3x+5y = 7 (ii)

we multiply (i) by 5 and (ii) by 3, we have

10x+15y = 25 (a)

9x+15y = 21 (b)

so (a) - (b) implies x = 4,

2) We do the same method for

{2x + y = 2

{3x + 4y = - 22,

and we found y = - 10,

3) for the last one,

{5x + 4y = 2

{-2y = 8 + 4x

this system is equivalent to

{5x + 4y = 2 (i)

{4x + 2y = - 8 (ii)

so, multiply (i) by 4 and (ii) by 5, and we have

20x + 16y = 8 (a)

20x + 10y = - 40 (b)

elimination of x gives 6y = 48 then y = 8, we can find x fastly by replacing y=8 in (i), so 5x + 4 (8) = 2, which implies x = - 6

finally the solution is S = { (-6, 8) }