Math  /  Algebra

QuestionFind the solution to the system of equations. You can use the interactive graph below to find the ss {y=4x3y=2x+1x=\begin{array}{l} \left\{\begin{array}{l} y=-4 x-3 \\ y=-2 x+1 \end{array}\right. \\ x=\square \end{array} \square y=y= \square

Studdy Solution

STEP 1

What is this asking? We need to find the values of xx and yy that satisfy *both* equations at the same time! Watch out! Don't mix up the xx and yy values – keep them straight!

STEP 2

1. Set the equations equal to each other
2. Solve for xx
3. Substitute xx back into either equation
4. Solve for yy

STEP 3

Since both equations are already solved for yy, we can set the *right-hand sides* equal to each other.
This gives us an equation with only xx, which we can solve!

STEP 4

4x3=2x+1-4x - 3 = -2x + 1

STEP 5

Why? To get all the xx terms on one side! 4x3+2x=2x+1+2x-4x - 3 + 2x = -2x + 1 + 2x 2x3=1-2x - 3 = 1

STEP 6

Why? To isolate the term with xx! 2x3+3=1+3-2x - 3 + 3 = 1 + 3 2x=4-2x = 4

STEP 7

Why? To get xx all by itself! 2x2=42\frac{-2x}{-2} = \frac{4}{-2} x=2x = -2So, x=2x = \mathbf{-2}!

STEP 8

We can choose either equation.
Let's use y=2x+1y = -2x + 1 because it looks a little simpler!

STEP 9

Let's plug in our **newly found** value of x=2x = -2. y=2(2)+1y = -2 \cdot (\mathbf{-2}) + 1

STEP 10

y=4+1y = 4 + 1 y=5y = 5 Awesome! We found y=5y = \mathbf{5}!

STEP 11

x=2x = -2 and y=5y = 5.
These values satisfy both equations, meaning they're true for both at the same time!

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