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:
- \( y = -3x + 4 \) (This equation is already in slope-intercept form.)
- \( y + 3x = -4 \)
Rewrite the second equation in slope-intercept form:
Starting with \( y + 3x = -4 \):
- Subtract \( 3x \) from both sides: \[ y = -3x - 4 \]
Now we have the two equations in slope-intercept form:
- \( y = -3x + 4 \)
- \( y = -3x - 4 \)
Graphing the Equations:
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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.
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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.