Question

Determine which numbers the equations can be multiplied by to create opposite terms of the x-variable. 1 2 x − 1 4 y = −3 − 1 3 x 2 3 y = 5 Which number can the first equation be multiplied by? Which number can the second equation be multiplied by?.

Answer 1

In the elimination method one variable is eliminated from the system of equation to find the value of other.

To create the opposite terms of the x-variable-

• First equation be multiplied by the number 12.
• Second equation be multiplied by the number 13.

What is elimination method?

To solve the system of equation and find the value of the variables, the elimination method is used.

In this method one variable is eliminated from the system of equation to find the value of other.

Given information-

The system of equation given in the problem is,

$12x-14y=-3$         ......1

Let the above equation as equation 1.

The second equation given in the problem is,

$-13x+23y=5$             ......2

Let the above equation as equation 2.

To eliminate the x term, make the coefficient of x of both the equation equal.

It can be done by multiply the coefficient of x term of first equation to second equation and coefficient of x term of second equation to first equation.

As the coefficient of x of the equation 1 is 12.  Thus multiply second equation with 12. Thus,

$12\times(-13x+23y)=12\times5$

$-156x+276y=60$                     ........3

Multiply  equation 1 with -13 to make the coefficient of x opposite. Thus,

$13\times(12x-14y)=13\times(-3)\\156x-182y=-39$         .......4

Hence, to create the opposite terms of the x-variable-

• First equation be multiplied by the number 12.
• Second equation be multiplied by the number 13.

Learn more about the elimination method here;

brainly.com/question/7013345

Answer 2

Answer:

First Equation:2

Second Equation:3

Step-by-step explanation:

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