Question

Solve the following system of equations.
9x+8y=-3
5x-2y=-21

Answer 1

Solving with substitution:

1. Express
`x` from first equation:

`9x+8y=-3`

`9x=-3-8y`

`x=(-3-8y)/(9)=-(3+8y)/(9)`

2. Replace
`x` in second equation with found value and solve it:

`5(-(3+8y)/(9))-2y=-21`

`-(15+40y)/(9)-2y=-21`

`-(15+40y)/(9)-(18y)/(9)=-21`

`(15+40y)/(9)+(18y)/(9)=21`

`(15+40y+18y)/(9)=21`

`(15+58y)/(9)=21`

`15+58y=21*9`

`58y=189-15`

`58y=174`

`y=(174)/(58)=3`

3. Replace
`y` in first equation with found value and solve it:

`9x+8*3=-3`

`9x+24=-3`

`9x=-3-24`

`9x=-27`

`x=(-27)/(3)=-9`

So,
`x=-9` and
`y=3`

Answer 2

9x+8y=-3
5x-2y=-21

multiply 2nd equation by 4
9x + 8y = -3
20x - 8y = -84
-----------------add
29x = -87
x = -3

9x+8y=-3
9(-3)+8y=-3
-27 + 8y = -3
8y = -3 +27
8y = 24
y = 3

answer
(-3,3)