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Solve this system of equations by graphing. First graph the equations, and then type the solution.

y=x–4
x=3
Click to select points on the graph.

1 answer

To graph the system of equations, we have:

  1. Equation 1: \(y = x - 4\)
  2. Equation 2: \(x = 3\)

Step 1: Graph the first equation, \(y = x - 4\).

This is a linear equation with a slope of 1 and a y-intercept of -4.

  • When \(x = 0\): \(y = 0 - 4 = -4\) (Point: (0, -4))
  • When \(x = 4\): \(y = 4 - 4 = 0\) (Point: (4, 0))

Plot these points and draw a line through them.

Step 2: Graph the second equation, \(x = 3\).

This is a vertical line where \(x\) is always 3. It intersects the x-axis at the point (3, y) for all values of \(y\).

Step 3: Determine the solution by finding the points of intersection.

To find the intersection, substitute \(x = 3\) into the first equation:

\[ y = 3 - 4 = -1 \]

So, the point of intersection is (3, -1).

Summary of the solution:

The solution to the system of equations is:

(3, -1)

You can verify this by substituting back into both original equations, and both should hold true.