Question

SOLVE THE SYSTEM OF EQUATION BY GRAPHING
y = - 3x + 4
y + 3x = - 4

Answer 1

To solve the system of equations by graphing, we first need to rewrite both equations in slope-intercept form (y = mx + b) and then graph them.

### Given Equations:

1. \( y = -3x + 4 \) (This equation is already in slope-intercept form.)
2. \( y + 3x = -4 \)

#### Rewrite the second equation in slope-intercept form:

Starting with \( y + 3x = -4 \):

1. Subtract \( 3x \) from both sides:
\[
y = -3x - 4
\]

### Now we have the two equations in slope-intercept form:
1. \( y = -3x + 4 \)
2. \( y = -3x - 4 \)

### Graphing the Equations:

1. **Graph \( y = -3x + 4 \)**:
- **Y-intercept**: (0, 4)
- **Slope**: -3 (which means for every 1 unit you move to the right, move 3 units down)
- Plot the intercept (0, 4) and then from there, move down 3 units and right 1 unit to get the point (1, 1).
- Draw the line.

2. **Graph \( y = -3x - 4 \)**:
- **Y-intercept**: (0, -4)
- **Slope**: -3 (same as the first equation)
- Plot the intercept (0, -4) and then from there, move down 3 units and right 1 unit to get the point (1, -7).
- Draw the line.

### Observing the Graph:
- The two equations are parallel lines since they both have the same slope (-3) but different y-intercepts (4 and -4).
- Since parallel lines do not intersect, there is **no solution** to this system of equations.

### Conclusion:
The system of equations \( y = -3x + 4 \) and \( y + 3x = -4 \) has no solution; the lines are parallel.