Question

how do I solve this system?
5x+4y=1
3x-4y=7

Answer 1

add them together the 4y will cancel and your left with 8x = 8 or x=1

Then plug x = 1 into any of the equations and you get y = -1

Answer 2

solve for why in both and set them equal to one another,

y = 1/4 -5x/4

y= 3x/4 - 7/4

3x/4 - 7/4 = 1/4 - 5x/4

solve for x

==> x = 1

plug x back into either of the original equation

y = 1/4 -5(1)/4 = -1

Answer 3

Adding the equations is a bit nicer in this case:
5x + 4y = 1
+ 3x - 4y = 7
===========
8x + 0y = 8

\[\implies 8x = 8 \implies x = 1.\]
Then plug in 1 to either original equation.