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

Question

please solve both ways and show steps.  thank you

Answer 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

 

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.

 

Answer 2

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