Question

solve the following system of equations graphically on the set of axes below.

\\y = -\frac{1}{6}x + 7\\
\\y = 2x - 6\\

plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Identify the equations

We are given the following system of linear equations to solve graphically:

$$
LATEXBLOCK0
$$

Find points for the first line

For the first equation, \(y = -\frac{1}{6}x + 7\):

• The \(y\)-intercept is \((0, 7)\).
• If \(x = 6\), then \(y = -\frac{1}{6}(6) + 7 = 6\), giving the point \((6, 6)\).
• If \(x = -6\), then \(y = -\frac{1}{6}(-6) + 7 = 8\), giving the point \((-6, 8)\).

Find points for the second line

For the second equation, \(y = 2x - 6\):

• The \(y\)-intercept is \((0, -6)\).
• If \(x = 3\), then \(y = 2(3) - 6 = 0\), giving the point \((3, 0)\).
• If \(x = 6\), then \(y = 2(6) - 6 = 6\), giving the point \((6, 6)\).

Determine the intersection point

By comparing the points calculated for both lines:

• Both lines pass through the point \((6, 6)\).
• Therefore, the solution to the system of equations is the intersection point \((6, 6)\).

Answer:

\((6, 6)\)