Question

Consider the system of equations \begin{align*} 5x + y &= 31, \\ -3x + 4y &= -37. \end{align*} Take your expression for $y$ from part (a), and substitute it into the second equation. Solve for $x$ and $y$. Enter your answer as the ordered pair $(x,y).$Please help! Thx!

Answer 1

Answer: (x, y) = (7, -4)

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Step-by-step explanation:

5x+y = 31 solves to y = -5x+31 after subtracting 5x from both sides.

We plug this into the other equation to get....

-3x + 4y = -37

-3x + 4( y ) = -37

-3x + 4( -5x+31 ) = -37 .... y replaced with -5x+31

-3x - 20x + 124 = -37 ... distribute

-23x+124 = -37

-23x = -37-124 .... subtract 124 from both sides

-23x = -161

x = -161/(-23) .... divide both sides by -23

x = 7

Use this x value to find y

y = -5x+31

y = -5(7)+31 ... plug in x = 7

y = -35+31

y = -4

The solution as an ordered pair is (x,y) = (7, -4)

If you graphed the original equations on the same xy grid, you should find they cross or intersect at (7, -4).