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Chapter 4: Q 14 (page 385)

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

2x-y=42x+3y=12

Short Answer

Expert verified

The solution of the system of linear equations is (3,2).

Step by step solution

01

Step 1. Given information

The linear equations are

2x-y=42x+3y=12

02

Step 2. Solving equations for the intersection 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=4-y=-2x+4y=2x-4Heretheslopeism=2Andthey-interceptisb=-4

Again find the slope and y-intercept by solving the Second equation for y

2x+3y=123y=-2x+12y=-23脳x+123y=-23x+4Heretheslopeism=-23Andthey-interceptisb=4

03

Step 3. Graph obtained

The solution of the system of linear equations is (3,2).

04

Step 4. Checking the equations

Firstsubstitutex=3,y=2intotheequation2x-y=42(3)-2=46-2=44=4Thisistrue.

Alsosubstitutex=3,y=2intotheequation2x+3y=122x+3y=122(3)+3(2)=126+6=1212=12Thisistrue.

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Most popular questions from this chapter

Translate to a system of equations and then solve:

Charlie left his mother鈥檚 house traveling at an average speed of 36miles per hour. His sister Sally left 15minutes (1/4hour)later traveling the same route at an average speed of miles per hour. How long before Sally catches

up to Charlie?

Without graphing, determine the number of solutions and then classify the system of equations.

(a)y=-2x-44x+2y=9(b)3x+2y=22x+y=1

A motor boat traveled 18miles down a river in two hours but going back upstream, it took 4.5 hours due to the current. Find the rate of the motor boat in still water and the rate of the current. (Round to the nearest hundredth).

The sum of two numbers is 65.

Their difference is 25. Find the

numbers.

Solve the systems of equations by substitution.

x-3y=-92x+5y=4
See all solutions

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