Question

What is the solution to this system of equations? {5x+4y=22 3x+4y=10

Answer 1

5x+4y=22.......eq 1
3x+4y=10.......eq 2
:
subtract equation 1 from equation 2
:
y terms are eliminated because 4y-4y=0. We are left with 5x-3x=22-10
:

2x=12
:

:
take the found value of x and plug it back into either equation
:
3(6)+4y=10--->18+4y=10--->4y=-8
:

Answer 2

multiply 2nd equqation by -1 and add to first

5x+4y=22
-3x-4y=-10 +
2x+0y=12

2x=12
divide by 2
x=6

sub back


3x+4y=10
3(6)+4y=10
18+4y=10
minus 18 both sides
4y=-8
divide by 4
y=-2

(x,y)
(6,-2) is solution