Graph the following system of equations.
\[
\begin{array}{r}
x+y=-5 \\
y=x-7
\end{array}
\]
Answer
The solution to the system of equations is the point where the two lines intersect. You can find this point by graphing the two lines on a piece of graph paper or using a graphing calculator or software. Plot the y-intercepts, use the slopes to find another point on each line, and then draw the lines. The point where they intersect is the solution to the system of equations.
Step 1 ：Rewrite the given equations in slope-intercept form (y = mx + b).
Step 2 ：The first equation is already in this form: \(x + y = -5\) => \(y = -x - 5\)
Step 3 ：The second equation is also in this form: \(y = x - 7\)
Step 4 ：Now, we can graph these two lines.
Step 5 ：For the first equation, \(y = -x - 5\), the slope is -1 and the y-intercept is -5. This means the line will cross the y-axis at -5 and for every step right, it will go one step down.
Step 6 ：For the second equation, \(y = x - 7\), the slope is 1 and the y-intercept is -7. This means the line will cross the y-axis at -7 and for every step right, it will go one step up.
Step 7 ：The solution to the system of equations is the point where the two lines intersect. You can find this point by graphing the two lines on a piece of graph paper or using a graphing calculator or software. Plot the y-intercepts, use the slopes to find another point on each line, and then draw the lines. The point where they intersect is the solution to the system of equations.
