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

1 Answer
Oct 16, 2016

Answer:

#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.