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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