Question

Solve the following system of equations:

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




1)(3, 1)
2)(-1, 3)
3)(-1, -3)
4)(1, 3)

Answer 1

The solution for the given system of equations is
`((-1)/(3),(1)/(3))`

Explanation:

Given system of equation

-2x + y = 1 ......(1)

4x + y = -1 ......(2)

We have to find the solution for the given system of equations.

We use elimination method,

In elimination method we make the coefficient of one variable same and then eliminate that variable by using suitable operation, and then solve for other variable.

Subtract equation (1) from (2) , we get,

⇒ 4x + y - ( -2x + y) = -1 - 1

⇒ 4x + y + 2x - y = -1 - 1

⇒ 4x + 2x = -2

⇒ 6x = -2

⇒
`x=(-1)/(3)`

Substitute
`x=(-1)/(3)` in (1) , we get,

`-2x + y = 1 \Rightarrow -2((-1)/(3) )+y=1 \Rightarrow ((2)/(3) ) + y = 1\\\\\Rightarrow y= 1-((2)/(3) ) \Rightarrow y=((1)/(3) )`

Thus, The solution for the given system of equations is
`((-1)/(3),(1)/(3))`

Answer 2

We have two equation with two unknowns. Therefore, we can solve the x and y easily. There are a number of methods to apply here but I will be using substitution method. We do as follows:

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

4x + y = -1
4x + 1 + 2x = -1
6x = -1 -1
6x = -2
x = -1/3

y= 1 + 2(-1/3)
y = 1/3