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Chapter 4: Q. 4.18 (page 380)

Solve the system by elimination:4x+y=-5-2x-2y=-2

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given Information. 

We have been given the system of equations4x+y=-5-2x-2y=-2.

02

Step 2. Eliminate y by multiplying a number in the first equation.

Multiply both sides of 4x+y=-5by 2.

2(4x+y)=2(-5)-2x-2y=-2

And,

localid="1644379547572" 8x+2y=-10-2x-2y=-2
03

Step 3. Add the equations resulting from Step 2 to eliminate one variable and solve it.

Add the x's,y'sand constants.

8x+2y=-10-2x-2y=-2

6x=-12

x=-2

04

Step 4. Substitute the solution from Step 3 into one of the original equation and solve for the other variable.

Substitute x=-2into the first equation.

4x+y=-5

4(-2)+y=-5

-8+y=-5

y=3

05

Step 5. Write the solution as an ordered pair.

Write it as (x,y).

(-2,3)

06

Step 6. Check that the ordered pair is a solution to both original equations.

Substitute x,y=-2,3into both original equations.

4x+y=-5

4(-2)+3=-5

-8+3=-5

-5=-5

And,

-2x-2y=-2

-2(-2)-2(3)=-2

4-6=-2

-2=-2

Both equations are True.

The point localid="1644918289518" (-2,3)is the solution to the system.

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Most popular questions from this chapter

Drew burned 1800 calories Friday playing one hour of basketball and canoeing for two hours. Saturday he spent two hours playing basketball and three hours canoeing and burned
3200 calories. How many calories did he burn per hour when playing basketball? How many calories did he burn per hour when canoeing?
  1. Solve the system of equations x+y=10x-y=6(a) by graphing (b) by substitution (c) Which method do you prefer? Why?

Translate to a system of equations and then solve:

Mark went to the gym and did 40minutes of Bikram hot yoga and 10minutes of jumping jacks. He burned 510calories. The next time he went to the gym, he did 30minutes of Bikram hot yoga and 20minutes of jumping jacks burning 470calories. How many calories were burned for each minute of yoga? How many calories were burned for each minute of jumping jacks?

Determine whether the ordered pair is a solution to the system x-3y=-8-3x-y=4

  1. (2,-2)
  2. (-2,2)

Solve the system by elimination:

3x-4y=-95x+3y=14
See all solutions

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