Question

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

Answer 1

To estimate the solution to the system of linear equations given by:

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

you can find the point where these two lines intersect graphically.

### Step 1: Identify y-intercepts

- For \( y = -5x + 7 \):
- The y-intercept is (0, 7).

- For \( y = -2x + 10 \):
- The y-intercept is (0, 10).

### Step 2: Identify slopes

- The slope of the first line is -5, which means it goes down steeply.
- The slope of the second line is -2, which means it goes down less steeply than the first line.

### Step 3: Estimate the point of intersection

You can also find the point of intersection algebraically by setting the two equations equal to each other:

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

### Solving the equation:

1. Rearranging gives:
\[
-5x + 2x = 10 - 7
\]
\[
-3x = 3
\]
\[
x = -1
\]

2. Substituting \( x = -1 \) back into either equation (let's use the second one):
\[
y = -2(-1) + 10 = 2 + 10 = 12
\]

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

### Conclusion

From the options provided:
- (12, -1)
- **(-1, 12)**
- (1, -12)
- (-1, -12)

The correct answer is **(-1, 12)**.