please solve both ways and show steps. thank you

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

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# 2 Answers

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

adding, gives

-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

adding

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.

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