Question

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Use this system of equations to answer the questions that follow.


4x – 9y = 7


–2x + 3y = 4


What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?


What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?

Answer 1

To eliminate the x-variable, we need to multiply by 2, to eliminate the y-variable, we need to multiply by 3.

How to simplify the system of equations?

Here we have the system:

4x - 9y = 7

-2x + 3y = 4

First, we want to find a number A such that when we write:

(4x - 9y) + A*(-2x + 3y) = 7 + A*4

(we just added the two equations, where we multiplied the second by A).

Now we want to eliminate the x-variable.

Then we must have:

(4 - 2A)*x = 0

So:

4 = 2A

4/2 = A  =  2

To eliminate the x-variable, we need to multiply the second equation by 2, and then add it to the first equation.

For the second part we do the same thing, but now we want to eliminate the y-variable, then we must have that:

(4x - 9y) + A*(-2x + 3y) = 7 + A*4

(-9 + 3A)*y = 0

Solving for A:

9 = 3A

9/3 = A = 3

This time, we need to multiply the second equation by 3.

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Answer 2

To eliminate the x-variable, we need to multiply by 2, to eliminate the y-variable, we need to multiply by 3.

What is system of equations?

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Here we have the system:

4x - 9y = 7

-2x + 3y = 4

First, we want to find a number A such that when we write:

(4x - 9y) + A X (-2x + 3y) = 7 + A X 4

(we just added the two equations, where we multiplied the second by A).

Now we want to eliminate the x-variable.

Then we must have:

(4 - 2A) X x = 0

So:

4 = 2A

4/2 = A  =  2

To eliminate the x-variable, we need to multiply the second equation by 2, and then add it to the first equation.

For the second part we do the same thing, but now we want to eliminate the y-variable, then we must have that:

(4x - 9y) + A X (-2x + 3y) = 7 + A X 4

(-9 + 3A) X y = 0

Solving for A:

9 = 3A

9/3 = A = 3

Thus, to eliminate the x-variable, we need to multiply by 2, to eliminate the y-variable, we need to multiply by 3.

Learn more about systems of equations from:

https://brainly.com/question/10413253

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