Question

Which constants could each equation be multiplied by to eliminate the x-variable using addition in this system of equations? 2x+3y=25 -3x+=22 first equation can be multiplied by –3 and the second equation by 2. The first equation can be multiplied by –4 and the second equation by 2. The first equation can be multiplied by 3 and the second equation by 2. The first equation can be multiplied by 4 and the second equation by –3.

Answer 1

1 equation multiples by 3
2 equation x by 2

Answer 2

The first equation can be multiplied by 3 and the second equation by 2.

Explanation:

Given

`2x+3y=25`

`-3x + y=22`

Required

How to eliminate x

To eliminate x using addition, we have to do the following;

1. Take the coefficient of x in equation 1; Coefficient = 2

2. Take the coefficient of x in equation 2; Coefficient = -3

3. Multiply equation 1 by 3

`3(2x + 3y = 25)`

`6x +9y = 75`

4. Multiply equation 2 by 2

`2(-3x + y = 22)`

`-6x + 2y = 44`

5. Add both resulting equations

`6x +9y = 75` +
`-6x + 2y = 44`

`6x - 6x + 9y + 2y = 75 + 44`

`11y = 75 + 44`

Notice that x has been eliminated;