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 =
+
123
+ 10

Answer 1

Let’s go through these steps to substitute \( y = 3x - 2 \) into the second equation and simplify.

We start with the given equations:

1. \( y = 3x - 2 \)
2. \( x = -2y + 10 \)

Now, we substitute \( 3x - 2 \) for \( y \) in the second equation:

\[ x = -2(3x - 2) + 10 \]

Next, we apply the distributive property to the right side of the equation:

\[ x = -2(3x) + (-2)(-2) + 10 \]

Now we multiply: \[ x = -6x + 4 + 10 \]

Next, we combine like terms on the right side:

\[ x = -6x + 14 \]

Now, we want to get all the \( x \) terms on one side. We can add \( 6x \) to both sides:

\[ x + 6x = 14 \] \[ 7x = 14 \]

Now, we divide both sides by 7:

\[ x = 2 \]

Now that we have the value of \( x \), we can substitute it back into the first equation to find \( y \):

\[ y = 3(2) - 2 \] \[ y = 6 - 2 \] \[ y = 4 \]

Thus, the solution to the system of equations is:

\[ (x, y) = (2, 4) \]