2x+3y=4

and

2x-5y=-12

Solve the given system by elimination and justify each step. Which procedure would not result in a system with a pair of opposite terms?

A) Multiply both sides of 2x + 3y = 4 by −1 and use the other equation to produce a system with a pair of opposite terms. This is an application of the multiplicative property of equality.

B) Multiply both sides of 2x − 5y = −12 by −1 and use the other equation to produce a system with a pair of opposite terms. This is an application of the multiplicative property of equality.

C) Multiply both sides of 2x − 5y = −12 by 3 and multiply both sides of 2x + 3y = 4 by 5 to produce a system with a pair of opposite terms. This is an application of the multiplicative property of equality.

D) Multiply both sides of 2x − 5y = −12 by −3 and multiply both sides of 2x + 3y = 4 by 5 to produce a system with a pair of opposite terms. This is an application of the multiplicative property of equality.

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calculista calculista · Answer 1 · 2019-12-27T09:04:52+01:00

Answer:

Option D

Step-by-step explanation:

we have

[tex]2x+3y=4[/tex] -----> equation A

[tex]2x-5y=-12[/tex] -----> equation B

Solve the system by elimination

Multiply both sides equation A by -1

[tex]-1(2x+3y)=-1(4)[/tex]

[tex]-2x-3y=-4[/tex] -----> equation C

Adds equation C and equation B

[tex]-2x-3y=-4\\2x-5y=-12\\------\\-3y-5y=-4-12\\-8y=-16\\y=2[/tex]

Find the value of x

substitute the value of y in either equation

[tex]2x+3(2)=4[/tex]

[tex]2x+6=4[/tex]

[tex]2x=-2[/tex]

[tex]x=-1[/tex]

The solution is the point (-1,2)

In this problem Option A,B and C are correct

The option D not result in a system with a pair of opposite terms

because

Multiply both sides of equation B by -3

[tex]-3(2x-5y)=-3(-12)[/tex]

[tex]-6x+15y=36[/tex] -----> equation C

Multiply both sides of equation A by 5

[tex]5(2x+3y)=5(4)[/tex]

[tex]10x+15y=20[/tex] ----> equation D

so

equation C and equation D not have a pair of opposite terms