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Chapter 5: Q 5.14. (page 587)

Solve each system by graphing:

y=3x-16x-2y=6

Short Answer

Expert verified

There is no solution to this system.

Step by step solution

01

Step 1. Given information 

The system of equations is

y=3x-16x-2y=6

02

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

The first equation is

y=3x-1

Compare with slope-intercept formula of a line

y=mx+b

So,

m=3b=-1

03

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

The second equation is

6x-2y=6

x-intercept:

6x-2脳0=66x-0=66x=66x6=66x=1

So, the x-intercept is (1,0)

y-intercept:

6脳0-2y=60-2y=6-2y=6-2y-2=6-2y=-3

So, the y-intercept is(0,-3)

04

Step 4. Graph the two lines.

First equation:

Slope is3

y-intercept is(0,-1)

Sketch the graph of line

Second equation:

Locate points(1,0),(0,-3) 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

Since no point is on both lines, there is no ordered pair that makes both equations true.

There is no solution to this system.

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