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Chapter 4: Q 4.7 (page 373)

Solve the system by graphing:y=-14x+2x+4y=-8

Short Answer

Expert verified

The system of equations y=-14x+2x+4y=-8has 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 equationsy=-14x+2x+4y=-8 and we need to find its solution by graphing.

02

Step 2. Graph the first equation.

The equation y=-14x+2is in slope-intercept form, so its slope is -14and its yintercept is 2.

So its graph is given as

03

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

Solving the equation x+4y=-8for ywe get,

localid="1644386022551" x+4y-x=-8-x4y=-x-84y4=-x-84y=-14x-2

So the slope of the line is -14and its yintercept is 2.

So the 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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