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Chapter 4: Q 332 (page 479)

In the following exercises, solve the following system of equations by graphing

2x-y=54x-2y=10

Short Answer

Expert verified

The solution to the linear equations infinitely many.

Step by step solution

01

Step 1. Given information

The given equations are

2x-y=54x-2y=10

02

Step 2. Finding intersecting points

First, solve both of these equations for y such that their slopes and y intercepts may be easily graphed.

And find the slope and y-intercept by solving the first equation for y.

2x-y=5-y=-2x+5y=2x-5Heretheslopeism=2Andthey-interceptisb=-5AgainSolvethesecondequationfory.andfindtheslopeandy-intercept.4x-2y=10-2y=-4x+10y=2x-5Heretheslopeism=2Andthey-interceptisb=-5

03

Step 3. Graph obtained

The lines are identical.

There are an endless number of ordered pairs that make both equations true because every point on the line does.

As a result, this system has an endless number of solutions.

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Most popular questions from this chapter

A motor boat travels60miles down a river in three hours but takes five hours to return upstream. Find the rate of the boat in still water and the rate of the current.

To decide whether it would be more convenient to solve the system of equations by substitution or elimination.

(a)y=4x+95x-2y=-21(b)9x-4y=243x+5y=-14

Translate to a system of equation and solve.

The difference of two supplementary angles is8 degrees. Find the measures of the angles.

Translate to a system of equations and then solve:

The difference of two complementary angles is 80degrees. Find the measures of the angles.

Solve the systems of equations by substitution.

5x-2y=-6y=3x+3
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