A coordinate plane with four quadrants shows the x-axis ranging from negative 10 to 10 in increments of 1 and the y-axis ranging from negative 5 to 15 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is y equals 4 x minus 10. The equation of the dotted line is y equals negative 2 x plus 8. The intersection point of both lines is shown at positive 3 on the x-axis and positive 2 on the y-axis in quadrant 1.

Question

Review the graphs of a system of these two linear equations in two variables: y=4x−10
and y=−2x+8
Find the solution of the system.

(1 point)
The solution of the system of equations is (
).

Answer 1

To find the solution of the system of equations given by

1. \( y = 4x - 10 \) (solid line)
2. \( y = -2x + 8 \) (dotted line)

we can set the two equations equal to each other to find the intersection point:

\[ 4x - 10 = -2x + 8 \]

Now, solve for \( x \):

1. Add \( 2x \) to both sides:

\[ 4x + 2x - 10 = 8 \] \[ 6x - 10 = 8 \]

2. Add 10 to both sides:

\[ 6x = 18 \]

3. Divide by 6:

\[ x = 3 \]

Now, substitute \( x = 3 \) back into either equation to find \( y \). We'll use the first equation:

\[ y = 4(3) - 10 = 12 - 10 = 2 \]

Thus, we have:

\[ (x, y) = (3, 2) \]

Therefore, the solution of the system of equations is:

\[ (3, 2) \]