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Find the ordered pair  that satisfies the system of equations

x + 3y = -4

3x - 7y = 36 + 5x - 2y

 Jan 23, 2022
 #1
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First we list the two equations.

 

\(x + 3y = -4 \)                    (1)

\(3x - 7y = 36 + 5x - 2y\) we must simplify the second equation to get:

\(-2x - 5y = 36\)               (2)

 

Now we have a system of equations that looks much nicer. On to the math:

 

First we multiply equation(1) by -2 to get:

\(-2x - 6y = 8\)                  (3) We will call this equation 3 for the sake of clarity.

 

Next we subtract equation(3) from equation(2) to cancel out variable x.

\(-2x - 5y - (-2x - 6y) = 36 - 8\) This simplifies to:

\(y = 28\)

 

Now we can plug the value of \(y\) back into equation(1) to get \(x\):

\(x + 84 = -4\) Then we subtract 84 from both sides of the equation to get x:

\(x = -88\)

 

Now we have the ordered pair of (x,y)

\(x = -88\)

\(y = 28\)

 

 

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 Jan 23, 2022

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