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Solve the system of equations by graphing. $\left\{\begin{array}{l} y=-x-1 \\ y=x+7 \end{array}\right.$
Use the graphing tool to graph the system. $\begin{array}{|c|c} \hline \text { Click to } \\ \text { enlarge } \\ \text { graph } \end{array}$ example Get more help -

Studdy Solution

STEP 1

1. The system of equations given is linear and can be solved by finding the intersection point of their graphs.
2. The equations are in slope-intercept form, which makes them easier to graph.
3. The solution involves plotting both equations on the same set of axes and identifying the point where they intersect.

STEP 2

1. Rewrite the equations to confirm they are in slope-intercept form.
2. Graph the first equation $y = -x - 1$ .
3. Graph the second equation $y = x + 7$ .
4. Identify the intersection point of the two lines.
5. Verify the solution by substituting the intersection point back into the original equations.

STEP 3

Rewrite the given equations to confirm they are in slope-intercept form, $y = mx + b$ :
For the first equation: $y = -x - 1$
For the second equation: $y = x + 7$

STEP 4

Graph the first equation $y = -x - 1$ by identifying its slope and y-intercept.
The slope $m$ is $-1$ and the y-intercept $b$ is $-1$ .
Plot the y-intercept point $(0, -1)$ and use the slope to find another point. For example, from $(0, -1)$ , move down 1 unit and right 1 unit to get another point $(1, -2)$ .
Draw the line passing through these points.

STEP 5

Graph the second equation $y = x + 7$ by identifying its slope and y-intercept.
The slope $m$ is $1$ and the y-intercept $b$ is $7$ .
Plot the y-intercept point $(0, 7)$ and use the slope to find another point. For example, from $(0, 7)$ , move up 1 unit and right 1 unit to get another point $(1, 8)$ .
Draw the line passing through these points.

STEP 6

Identify the intersection point of the two lines by determining where they cross on the graph.
By graphing the lines, we observe that they intersect at the point $(-4, 3)$ .

STEP 7

Verify the intersection point $(-4, 3)$ by substituting it back into the original equations.
For $y = -x - 1$ : $3 = -(-4) - 1$ $3 = 4 - 1$ $3 = 3$
For $y = x + 7$ : $3 = -4 + 7$ $3 = 3$
Both equations are satisfied by the point $(-4, 3)$ , confirming it is the correct solution.
Therefore, the solution to the system of equations is: $(-4, 3)$

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