Question

Estimate the solution to the system of these linear equations based on the graph.
y =-5x + 7
y = -2x + 10 (1 point)
• (-1, 12)
O (12, -1)
O (1, -12)
• (-1,-12)

Answer 1

To estimate the solution to the system of linear equations by analyzing the equations provided, we can find the intersection point of the two lines represented by the equations:

1. \(y = -5x + 7\)
2. \(y = -2x + 10\)

**Step 1: Solve the equations simultaneously**

Set the equations equal to each other since at the point of intersection, the two equations will yield the same \(y\):

\[
-5x + 7 = -2x + 10
\]

**Step 2: Rearranging the equation**

Add \(5x\) to both sides:

\[
7 = 3x + 10
\]

Subtract \(10\) from both sides:

\[
-3 = 3x
\]

Now, divide by \(3\):

\[
x = -1
\]

**Step 3: Substitute \(x\) back to find \(y\)**

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

\[
y = -2(-1) + 10
\]
\[
y = 2 + 10 = 12
\]

Thus, the intersection point is \((-1, 12)\).

**Review the answer choices:**

- (-1, 12) (correct)
- (12, -1)
- (1, -12)
- (-1, -12)

The solution to the system of equations based on the calculations we just did is **(-1, 12)**.