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SOLVE THE SYSTEM OF EQUATION BY GRAPHING

y = - 3x + 4
y + 3x = - 4

1 answer

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.