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Chapter 15: Problem 2

Solve each system graphically. $$ \begin{aligned} &x-y=1\\\ &x+y=3 \end{aligned} $$

Short Answer

Expert verified
The solution is \((2, 1)\).

Step by step solution

01

Rewrite Equations in Slope-Intercept Form

To graph each equation, rewrite them in slope-intercept form ( \(y = mx + b\)). For the first equation \(x - y = 1\), solve for \(y\): \(y = x - 1\). For the second equation \(x + y = 3\), solve for \(y\): \(y = -x + 3\).
02

Graph the First Equation

Graph the equation \(y = x - 1\). Start by plotting the y-intercept (0, -1). Then, use the slope, which is 1, to find another point on the line. From (0, -1), go up 1 unit and to the right 1 unit to plot the point (1, 0). Draw a line through these points.
03

Graph the Second Equation

Graph the equation \(y = -x + 3\). Start by plotting the y-intercept (0, 3). Then, use the slope, which is -1, to find another point on the line. From (0, 3), go down 1 unit and to the right 1 unit to plot the point (1, 2). Draw a line through these points.
04

Find the Intersection

Identify the point where the two lines intersect. The lines \(y = x - 1\) and \(y = -x + 3\) intersect at the point (2, 1). This is the solution to the system of equations.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

slope-intercept form
The slope-intercept form of a linear equation is one of the most popular ways to express a straight line. It is written as \(y = mx + b\), where:
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