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.

To find the solution to the system of equations given by:

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

we first need to find the point where these two lines intersect. This point will be the solution to the system of equations.

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

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

Next, we 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 that we have the value of \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use the first equation:

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

So, the solution to the system of equations, or the point of intersection of the two lines, is:

\[ (3, 2) \]

Thus, the solution to the system of equations is \( (3, 2) \).

Yes, I am confident in the solution. To verify, let’s check that the coordinates \((3, 2)\) satisfy both equations.

1. For the first equation \(y = 4x - 10\):

   • Substitute \(x = 3\): \[ y = 4(3) - 10 = 12 - 10 = 2 \]
   • This holds true, so the point is on the line represented by the first equation.

2. For the second equation \(y = -2x + 8\):

   • Substitute \(x = 3\): \[ y = -2(3) + 8 = -6 + 8 = 2 \]
   • This also holds true, so the point is on the line represented by the second equation.

Since both equations are satisfied by the point \((3, 2)\), the solution to the system of equations is indeed \((3, 2)\). If you have any further questions, feel free to ask!