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Chapter 7: Problem 9

Solve each system by graphing. Check the coordinates of the intersection point in both equations. \(\left\\{\begin{array}{l}y=x+5 \\ y=-x+3\end{array}\right.\)

Short Answer

Expert verified
The solution of this system of equations by graphing is \(-1, 4\). After checking this point in both equations, it's clear that it is indeed the correct solution.

Step by step solution

01

Plot the first equation

Firstly, the equation \(y=x+5\) is plotted on the graph. This line has a slope of 1 and it crosses the y-axis at 5.
02

Plot the second equation

Next, the equation \(y=-x+3\) is also plotted on the same graph. This line has a slope of -1 and it crosses the y-axis at 3.
03

Find intersection point

The solution to the system is the coordinates of the point at which the two lines intersect. After plotting both equations, it's clear that they intersect at the point \(-1, 4\), and this is therefore the solution of the system.
04

Check intersection point

Substitute \(-1\) for \(x\) and \(4\) for \(y\) into both equations to check. For the first equation: \(y = -1 + 5 = 4\) and for the second equation: \(y = --1 + 3 = 4\). Since the results are true for both equations, the solution is valid.

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