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Chapter 5: Q 5.16. (page 588)

Solve each system by graphing:

y=12x-42x-4y=16

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=12x-42x-4y=16

02

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

The first equation is

y=12x-4

Compare with the slope-intercept formula of a line

y=mx+b

So,

m=12b=-4

03

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

The second equation is

2x-4y=16

x-intercept:

2x-4脳0=162x-0=162x=162x2=162x=8

So, the x-intercept is (8,0)

y-intercept:

2脳0-4y=16-4y=16-4y-4=16-4y=-4

So, the y-intercept is(0,-4)

04

Step 4. Graph the two lines.

First equation:

Slope is12

y-intercept is(0,-4)

Second equation:

Locate points(8,0),(0,-4) 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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Most popular questions from this chapter

In the following exercises, translate to a system of equations and solve.

Mitchell currently sells stoves for company A at a salary of \(12,000 plus a \)150 commission for each stove he sells. Company B offers him a position with a salary of \(24,000 plus a \)50 commission for each stove he sells. How many stoves would Mitchell need to sell for the options to be equal?

Solve a System of Equations by Elimination -

5x-3y=-12x-y=2

Determine whether an ordered pair is a solution of a system of equations. In the following exercises, determine if the following points are solutions to the given system of equations.

2x+y=5x+y=1

(a)(4,-3)

(b)(2,0)

In the following exercises, translate to a system of equations and solve.

Shelly spent 10 minutes jogging and 20 minutes cycling and burned 300 calories. The next day, Shelly swapped times, doing 20 minutes of jogging and 10 minutes of cycling and burned the same number of calories. How many calories were burned for each minute of jogging and how many for each minute of cycling?

In the following exercises, solve the following systems of equations by graphing.

x+y=4x-y=0
See all solutions

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