Question

PLEASE HELP :(

Given the system of linear equations. Choose all of the options that could be used to solve the system using addition
(x + y = 7
12x + y = 5
Multiply the first equation by-1 and add the equations together.
Multiply the second equation by -1 and the first equation by -1, then add the equations together.
Multiply the second equation by -1 and add the equations together.
Multiply the first equation by -2 and add the equations together.
Multiply the first equation by 2 and the second equation by -1, then add the equations together.

Answer 1

First option: Multiply the first equation by-1 and add the equations together.

Third option: Multiply the second equation by -1 and add the equations together.

Explanation:

The method to solve a system of equations using addition is known as Elimination Method.

The idea is to get an equation with one variable, solve for that variable to find its value and the substitute this into any original equation to find the value of the other variable.

In this case, multiplying the first equation by -1, you get:

`\left \{ {{-x -y =-7} \atop {12x + y = 5}} \right.\\.................\\11x=-2\\\\x=-5.5`

`x + y = 7\\\\-5.5+y=7\\\\y=12.5`

Multiplying the second equation by -1, you get:

`\left \{ {{x + y = 7} \atop {-12x - y = -5}} \right.\\.................\\-11x=2\\\\x=-5.5`

`x + y = 7\\\\-5.5+y=7\\\\y=12.5`

Answer 2

The options that could be used to solve the system of linear equations are:

1. Multiply the first equation by -1 and add the equations together.

2. Multiply the second equation by -1 and add the equations together.

Explanation:

Given two equations, what we need to solve them is apply some operations on each of them and add them in such a way that one of the variables cancels each other. Then we can simply solve for the other variable.

We have:

x + y = 7

12x + y = 5

We can multiply equation 1 by -1 and add the equations and then solve for x:

(-1)(x+y)=(-1)(7)

-x-y = -7 Now add it in equation 2:

-x-y + 12x+y = 5+7

11x = 12

x = 12/11

Then put x = 12/11 in one of the equations to get y.

Similarly we can multiply equation 2 by -1 and add the equations and follow the same steps afterwards.