Question

Given the following system of equations: 2x + 6y = 12 4x + 3y = 15 Which action creates an equivalent system that will eliminate one variable when they are combined? Multiply the second equation by −2 to get −8x − 6y = −30. Multiply the first equation by 2 to get 4x + 12y = 24. Multiply the second equation by −4 to get −16x − 12y = −60. Multiply the first equation by −4 to get −8x − 24y = −48.

Answer 1

Option A and B are correct.

Step-by-step explanation:

We are given the following systems of equation:

$2x + 6y = 12 \\4x + 3y = 15$

We need to identify the action creates an equivalent system that will eliminate one variable when they are combined.

Checking the options:

a) Multiply the second equation by −2 to get −8x − 6y = −30

If we add equation(1) and the new equation(2) the variable y will be eliminated. So, this is the correct option.

b)  Multiply the first equation by 2 to get 4x + 12y = 24.

If we subtract new equation(1) and equation(2), the variable x will be eliminated. So, this is the correct option.

c) Multiply the second equation by −4 to get −16x − 12y = −60

By adding or subtracting, none of the variable is eliminated. So, it is not the correct option.

d) Multiply the first equation by −4 to get −8x − 24y = −48.

By adding or subtracting, none of the variable is eliminated. So, it is not the correct option.

So, Option A and B are correct.

Keywords: Solve System of equations

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Answer 2

Answer:

Multiply the second equation by −2 to get −8x − 6y = −30.

Step-by-step explanation:

we have

----> first equation

----> second equation

Solve by elimination

Multiply the second equation by -2 both sides

---> equivalent second equation

Adds first equation and the equivalent second equation

Find the value of y

substitute the value of x in any of the equation

the solution of the system is the point (3,1)