Question

If 2x + 3y = 17 and 3x + 4y = 24, then 5x +7y =

Answer 1

solve for x and y

Answer 2

x = 4
y = 3

now solve
5x +7y =

Answer 3

Set up your system of equations so that it is easier to see what is happening.

2x+3y=17
3x+4y=24

You want to manipulate one or the other (or even both) so that a cancellation is possible when you "combine" the equations.

-3(2x+3y=17) = -6x-9y=-51
2(3x+4y=24) = 6x+8y= 48

All I did is multiply the top eq by (-3) and multiply the bottom eq by (2). Notice when we "combine" the two resulting equations, the (-6x) and the (6x) give us ZERO. The X variable is gone.

Therefore

-1y=-3

or

y=3.

Now you can substitute this value of Y into the first OR the second equation to solve for X. Then you will know both values.

You can handle it form here.