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# how do you solve the linear equation 4x - y = 5 and 4x + 4y = -4 using substituation AND elimination

please solve both ways and show steps.  thank you

### 2 Answers by Expert Tutors

Glenn M. | Math and Science TutorMath and Science Tutor
4.9 4.9 (408 lesson ratings) (408)
1
using substitution :

solve for one of the unknowns in one of the equations and substitute into the other equation.

y=4x-5  solving for y in the 1st equation

using this in the 2nd equation

4x+4(4x-5)=-4
4x+16x-20=-4
20x=16
x=16/20=4/5

substitute back into either equation

y=4(4/5)-5
y=-(9/5)

x=4/5  and y = -(9,5)

Elimination :
multiply the 2nd equation by -1

4x-y=5
-4x-4y=4

-y-4y=5+4    the 4x and the -4x on the left side cancel
-5y=9
y=-(9/5)

now calculate x, either sub into the either equation or can multiply the 1st equation by 4 and add again

16x-4y=20
4x+4y=-4

16x+4x=20-4    the -4y and the +4y cancel
20x=16
x=16/20=4/5

same value for x and y as we had before.
Can substitute the answer into the original equation and check to see that we didn't make any mistakes.

Steve P. | Patient and Knowledgable Math and Chemistry TutorPatient and Knowledgable Math and Chemis...
4.8 4.8 (5 lesson ratings) (5)
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Substitution

Rearrange one of the equations:

y=4x-5

Substitute into the other equation:

4x+4(4x-5)=-4

4x+16x-20=-4

20x=16

x=4/5

Substitute into one of the original equations to solve for y:

y=4(4/5)-5

=16/5-25/5= -9/5

Elimination

Subtract to eliminate one of the variables:

4x-y=5
4x+4y=-4
---------------
-5y=9

y=-9/5

Substitute

4x-(-9/5)=5

4x=25/5-9/5

x=(16/5)/4

x=4/5