Question

How do you solve the following system?: `7x +5y =-15 , -4x -9y = 5`

Answer 1

`x = -2 24/43, " "y = 25/43`

Explanation:

There is no single variable, so using the method of substitution will lead to some uncomfortable math.

Let's use the elimination method.

`color(white)(xxxxxxxxx)7x +5y = -15`...........................A
`color(white)(xxxxxxx)-4x -9y = +5`..............................B

Make additive inverses. I have chosen the x terms for this.

`A xx4" "28x+20y = -60`........................C
`B xx7" "-28x-63y = +35`........................D

`C+D" "-43y = -25`

`color(white)(xxxxxxxxxxxxxxx) y =25/43`

Substitute `y= 25/43` in A

`7x + 5xx(25/43) = -15`

`7x = -15 -125/43`

`7x = -17 39/43`

`x = -2 24/43`

Substituting for x and y in B gives 5.

Despite the awkward fractions, the method remains the same.