Math  /  Geometry

QuestionSolve the following system of equations graphically on the set of axes below y=13x1y=x+7\begin{array}{c} y=-\frac{1}{3} x-1 \\ y=x+7 \end{array}
Plot two lines by clicking the graph. Click a line to delete it.

Studdy Solution

STEP 1

1. The system consists of two linear equations.
2. The solution to the system is the point where the two lines intersect.

STEP 2

1. Identify the equations of the lines.
2. Determine the slope and y-intercept for each line.
3. Plot the first line using its slope and y-intercept.
4. Plot the second line using its slope and y-intercept.
5. Identify the point of intersection.

STEP 3

Identify the equations of the lines:
Equation 1: y=13x1 y = -\frac{1}{3}x - 1
Equation 2: y=x+7 y = x + 7

STEP 4

Determine the slope and y-intercept for each line:
For Equation 1: - Slope (m1m_1) = 13-\frac{1}{3} - Y-intercept (b1b_1) = 1-1
For Equation 2: - Slope (m2m_2) = 11 - Y-intercept (b2b_2) = 77

STEP 5

Plot the first line using its slope and y-intercept:
1. Start at the y-intercept (0,1)(0, -1).
2. Use the slope 13-\frac{1}{3} to find another point. Move down 1 unit and right 3 units to point (3,2)(3, -2).
3. Draw a line through these points.

STEP 6

Plot the second line using its slope and y-intercept:
1. Start at the y-intercept (0,7)(0, 7).
2. Use the slope 11 to find another point. Move up 1 unit and right 1 unit to point (1,8)(1, 8).
3. Draw a line through these points.

STEP 7

Identify the point of intersection:
1. Observe where the two lines intersect on the graph.
2. The intersection point is the solution to the system of equations.

The solution to the system of equations is the point of intersection:
(3,4) \boxed{(-3, 4)}

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