solve the given system of equations by the equations by the substitution method; -8x - 6y = -82 and y= 4x-29

Question

Solve x and y

Answer 1

-8x - 6y = -82

y = 4x - 29

 

-8x - 6(4x - 29) = -82      substitute

 

Now distribute and solve for x.

Then substitute the value for x in either equation and solve for y.

Answer 2

-8x - 6y = -82 and y = 4x - 29

 

Since the second equation is y = substitute 4x - 29 into the first equation

 

-8x - 6(4x - 29) = -82 use distribution property

 

-8x - 24x + 174 = -82 Combine like terms

 

-32x + 174 = -82 get constants on right side

 

-32x + 174 - 174 = -82 - 174

-32x = -256 Divide both sides by -32

 

-32x/-32x = -256/-32

x = 8 Substitute into 2nd equation to go directly to y

 

y = 4(8) - 29

y = 32 - 29

y = 3

 

Solution is (8,3)

 

Substitute into both equations to check.

 

-8(8) - 6(3) = -82 and 3 = 4(8) - 29

-64 - 18 = -82      and 3 = 32 - 29

-82 = -82             and 3 = 3 check

 

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