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Chapter 5: Q 5.15. (page 587)

Solve each system by graphing:

y=-3x-66x+2y=-12

Short Answer

Expert verified

There are infinitely many solutions to this system.

Step by step solution

01

Step 1. Given information 

The system of equations is

y=-3x-66x+2y=-12

02

Step 2. Find the slope and y-intercept of the first equation

The first equation is

y=-3x-6

Compare with slope-intercept formula of a line

y=mx+b

So,

m=-3b=-6

03

Step 3. Find the x and y-intercept of the second equation

The second equation is

6x+2y=-12

x-intercept:

6x+12脳0=-126x+0=-126x=-126x6=-126x=-2

So, the x-intercept is (-2,0)

y-intercept:

role="math" localid="1647774730304" 6脳0+2y=-122y=-1212y2=-122y=-6

So, the y-intercept is(0,-6)

04

Step 4. Graph the two lines.

First equation:

Slope is-3

y-intercept is(0,-6)

Second equation:

Locate points(-2,0),(0,-6) on the graph and then join them to get the graph

So, the graph is

05

Step 5. Determine the point of intersection.

The graph is

The lines are the same!

Since every point on the line makes both equations true,

there are infinitely many ordered pairs that make both equations true.

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