Question

Solve the following system of equations.

can you please show all the steps to complete this problem
7x + 4y = -8 -8x - 5y = 13
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Answer 1

x=4 and y=−9

Explanation:

Problem:

Solve 7x+4y=−8;−8x−5y=13

Steps:

I will solve your system by substitution.

(You can also solve this system by elimination.)'

7x+4y=−8;−8x−5y=13

Step: Solve 7x+4y=−8 for x:

7x+4y+−4y=−8+−4y(Add -4y to both sides)

7x=−4y−8

7x/7 = -4y-8/7 (Divide both sides by 7)

x=-4/7y + -8/7

Step: Substitute -4/7y + -8/7 for x in −8x−5y=13:

−8x−5y=13

-8(-4/7y + -8/7) −5y=13

-3/7y + 64/7 =13(Simplify both sides of the equation)

-3/7y + 64/7 + -64/7 = 13 + -64/7 (Add (-64)/7 to both sides)

-3/7y = 27/7

-3/7y/-3/7 = 27/7/-3/7 (Divide both sides by (-3)/7)

y=−9

Step: Substitute −9 for y in x= -4/7y + -8/7:

x = -4/7y + -8/7

x = -4/7 (-9) + -8/7

x=4(Simplify both sides of the equation)

Answer:

x=4 and y=−9

Answer 2

7x + 4y = -8 (1)
-8x - 5y = 13 (2)

(2) + (1)
(-8x-5y)+(7x+4y) = (13)+(-8)
-8x-5y+7x+4y = 5
-x-y = 5 (3)

(3)x4
-4x-4y = 20 (4)

(4) + (1)
(-4x-4y)+(7x+4y) = (20)+(-8)
-4x-4y+7x+4y = 12
3x = 12
x = 4

Sub x=4 into (4)
-4x-4y = 20
-4(4)-4y = 20
-4y = 36
y = -9

Therefore x=4, y=-9.