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Chapter 4: Q 4.8 (page 373)

Solve the system by graphing: y=3x-16x-2y=6

Short Answer

Expert verified

The system of equations y=3x-16x-2y=6has no solution and it can be seen in the graph as,

Step by step solution

01

Step 1. Given Information.

We are given a system of equations y=3x-16x-2y=6and we need to find its solution by graphing.

02

Step 2. Graph the first equation.

The equation y=3x-1is in slope-intercept form, so its slope is 3 and its yintercept is -1.

So its graph is given as

03

Step 3. Graph the second equation on the same rectangular coordinate system.

Solving the equation 6x-2y=6for ywe get,

6x-2y-6x=6-6x-2y=-6x+6-2y-2=-6x+6-2y=3x-3

So the slope of the line is 3and its yintercept is -3.

So its graph can be drawn on the same plane as

04

Step 4. Identify the solution to the system.

  • From the graph, it can be seen that the lines are parallel.
  • Since no point is on both lines, there is no ordered pair that makes both equations true.
  • There is no solution to the given system.

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