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

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Answer 1 · 2016-10-16T07:29:47

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

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.

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