Math  /  Algebra

QuestionSolve the system of equations graphed on the coordinate axes bel y=2x+8y=3x7\begin{array}{l} y=2 x+8 \\ y=-3 x-7 \end{array}

Studdy Solution

STEP 1

What is this asking? We need to find the (x,y)(x, y) point where the lines y=2x+8y = 2x + 8 and y=3x7y = -3x - 7 cross! Watch out! Make sure your signs are correct when solving for xx and yy!

STEP 2

1. Set the equations equal to each other.
2. Solve for xx.
3. Substitute xx back into one of the original equations to solve for yy.

STEP 3

Since both equations are equal to yy, they must be equal to each other at the point where the lines intersect.
This is the big idea!

STEP 4

2x+8=3x72x + 8 = -3x - 7

STEP 5

We want to get all the xx terms on one side.
Adding 3x3x to both sides gives us: 2x+3x+8=3x+3x72x + 3x + 8 = -3x + 3x - 7 5x+8=75x + 8 = -7

STEP 6

Now, let's isolate the xx term by subtracting 8 from both sides: 5x+88=785x + 8 - 8 = -7 - 8 5x=155x = -15

STEP 7

Finally, divide both sides by **5** to find our **xx value**: 5x5=155\frac{5x}{5} = \frac{-15}{5} x=3x = -3 Woohoo!
We found xx!

STEP 8

Let's use the first equation, y=2x+8y = 2x + 8, because it looks a little friendlier.
But either equation would work!

STEP 9

Substitute our **xx value**, 3-3, into the equation: y=2(3)+8y = 2 \cdot (-3) + 8 y=6+8y = -6 + 8y=2y = 2Yes! We found our **yy value**!

STEP 10

The solution to the system of equations is the point where the lines intersect, which is (3,2)(-3, 2).

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