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Chapter 5: Q 5.7. (page 584)

Solve each system by graphing:

-x+y=12x+y=10

Short Answer

Expert verified

The solution is(3,4)

Step by step solution

01

Step 1. Given information 

The system of equations is

-x+y=12x+y=10

02

Step 2. Find the slope and y-intercept of both equations.

First equation:

-x+y=1

Solve for y

-x+y+x=1+xy=x+1

Compare with the slope-intercept formula of line

y=mx+b

So,

m=1b=1

Second equation:

2x+y=10

Solve for y

2x+y=102x+y-2x=10-2xy=-2x+10

Compare with the slope-intercept formula of line

y=mx+b

So,

m=-2b=10

03

Step 3. Graph the two lines.

First equation:

Slope is1

y-intercept is1

Second equation:

Slope is-2

y-intercept is10

Sketch the graph of equations using slope and intercept

So, the graph is

04

Step 4. Determine the point of intersection.

The graph is

Since the intersection point is (3,4)

So, the solution is(3,4)

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