Question

Solve the following system of equations: −2x + y = 1 −4x + y = −1

A.(3, 1)
B.(−1, 3)
C.(−1, −3)
D.(1, 3)

Answer 1

Hello!

-2x + y = 1
-4x + y = -1

You can subtract these equations from each other to eliminate y

2x = 2

Divide both sides by 2

x = 1

Put this into one of the original equations

-2(1) + y = 1

Combine like terms

-2 + y = 1

Add 2 to both sides

y = 3

The answer is D) (1, 3)

Hope this helps!

Answer 2

d. (1,3)

Explanation:

We will use the substitution method to solve this system of linear equations with two unknowns.

First, we will have to choose any variable from some equation and clear it.

I will use the first equation, with the variable "y"

`-2x+y=1\\y=1+2x`

We will substitute this equation in the second equation. Every time we find the value of "y", let's replace.

`-4x+y=-1\\-4x+(1+2x)=-1`

We will solve this equation to find the value of "x"

`-4x+1+2x=-1\\-2x=-1+1\\-2x=-2\\x=(-2)/(-2) \\x=1`

Now, the found value of "x" will replace it in any of my two initial equations.

`-2(1)+y=1\\`

and we solve

`-2+y=1\\y=1+2\\y=3`

Thus, the result of this system of equations is

(1,3)