Question

Graph the system of equations on graph paper to answer the question.



{y=2x+7y=−4x−5



What is the solution for the system of equations?

Answer 1

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

1. \( y = 2x + 7 \)
2. \( y = -4x - 5 \)

we can graph both equations and determine their point of intersection.

### Step 1: Graph the first equation \( y = 2x + 7 \)

1. Find the y-intercept: When \( x = 0 \), \( y = 2(0) + 7 = 7 \). So the point (0, 7) is on the graph.
2. Find another point. For \( x = 1 \), \( y = 2(1) + 7 = 9 \). So the point (1, 9) is also on the graph.
3. Plot these points and draw the line.

### Step 2: Graph the second equation \( y = -4x - 5 \)

1. Find the y-intercept: When \( x = 0 \), \( y = -4(0) - 5 = -5 \). So the point (0, -5) is on the graph.
2. Find another point. For \( x = 1 \), \( y = -4(1) - 5 = -9 \). So the point (1, -9) is also on the graph.
3. Plot these points and draw the line.

### Step 3: Find the Intersection

To find the solution to the system, we can set the two equations equal to each other since they both equal \( y \):

\[ 2x + 7 = -4x - 5 \]

### Step 4: Solve for x

1. Combine like terms:
\[ 2x + 4x = -5 - 7 \]
\[ 6x = -12 \]
\[ x = -2 \]

### Step 5: Find y using one of the equations

Plug \( x = -2 \) back into one of the original equations, preferably \( y = 2x + 7 \):

\[ y = 2(-2) + 7 \]
\[ y = -4 + 7 \]
\[ y = 3 \]

### Conclusion

The solution to the system of equations is \( (x, y) = (-2, 3) \).

### Summary
The intersection point of the two lines on the graph represents the solution to the system of equations, which is \( (-2, 3) \).