Question

Solve the system of equations using any method.

y = -3x + 5 and y = 6x + 2
Responses

A (3, 3)(3, 3)

B (-3, 1)(-3, 1)

C (-3, -1)(-3, -1)

D (

, 4)( 1 3 , 4) Solve the system of equations using any method.

y = -3x + 5 and y = 6x + 2
Responses

A (3, 3)(3, 3)

B (-3, 1)(-3, 1)

C (-3, -1)(-3, -1)

D (

, 4)( 1 3 , 4)

Answer 1

To solve the system of equations:

1. \( y = -3x + 5 \)
2. \( y = 6x + 2 \)

We can set the two equations equal to each other since both are equal to \( y \):

\[
-3x + 5 = 6x + 2
\]

Now, let's solve for \( x \):

1. Add \( 3x \) to both sides:

\[
5 = 9x + 2
\]

2. Subtract \( 2 \) from both sides:

\[
3 = 9x
\]

3. Divide by \( 9 \):

\[
x = \frac{3}{9} = \frac{1}{3}
\]

Now that we have found \( x \), we can substitute it back into either of the original equations to find \( y \). Let's use the first equation:

\[
y = -3\left(\frac{1}{3}\right) + 5
\]
\[
y = -1 + 5
\]
\[
y = 4
\]

So the solution to the system of equations is:

\[
\left( \frac{1}{3}, 4 \right)
\]

Looking at the choices provided, the appropriate response is:

**D** \( \left( \frac{1}{3}, 4 \right) \)