Find the solution to the system of equations below.

Question

Start by looking at the two equations in the system. What does the first equation tell you about the variable y?
The variable y equals
3x−2
.
Nice!
The first equation tells you that y equals 3x−2. So, one way to start solving this system of equations is to substitute 3x−2 anywhere you see y in the second equation. Go for it. Substitute 3x−2 for y in the second equation.
y= 3x−2
x= −2y+10
x = −2(
) + 10
You got it!
We want to get the x terms alone on one side of the equation, but right now x is inside parentheses on the right. Use the distributive property to multiply −2 and 3x−2 to rewrite the right side of the equation without parentheses. You can think of −2(3x−2) as −2(3x+−2). So, you can multiply -2 by 3x, then add the product of -2 and −2. Start by multiplying -2 by 3x.
y= 3x−2
x= −2y+10
x = −2(3x−2) + 10
x = -2(3x + −2) + 10
x =
+
?
+ 10

Answer 1

Let's work through the problem step by step.

1. We have the first equation as: \[ y = 3x - 2 \]

2. We also have the second equation: \[ x = -2y + 10 \]

3. We substitute \( y = 3x - 2 \) into the second equation: \[ x = -2(3x - 2) + 10 \]

4. Now we will use the distributive property to eliminate the parentheses: \[ x = -2(3x) + -2(-2) + 10 \]

5. This simplifies to: \[ x = -6x + 4 + 10 \]

6. Now combine the constants (4 + 10): \[ x = -6x + 14 \]

7. To isolate \( x \), let's add \( 6x \) to both sides of the equation: \[ x + 6x = 14 \] \[ 7x = 14 \]

8. Now divide both sides by 7: \[ x = 2 \]

9. Now that we have \( x \), we can substitute it back into the first equation to find \( y \): \[ y = 3(2) - 2 \] \[ y = 6 - 2 \] \[ y = 4 \]

So the solution to the system of equations is: \[ (x, y) = (2, 4) \]