Question

3x + y = 0x - y =4solve using the substitution method for the linear equation

Answer 1

We have a system of linear equations that we have to solve by substitution. This method consists of clearing one variable from one of the equations, and substituting its value in the other equation (for the case of 2 variables).

We can use any of the equations to start. We will pick the second one, as it is easier.

We will clear the value of x:

`x-y=4\Rightarrow x=4+y`

Now that we have an expression for x, we replace it in the second equation and solve for y as:

`\begin{gathered} 3x+y=0 \\ 3(4+y)+y=0 \\ 12+3y+y=0 \\ 12+4y=0 \\ 4y=-12 \\ y=-(12)/(4) \\ y=-3 \end{gathered}`

Now, we have the value of y, so we can calculate the value of x using the substitution we have calculated earlier:

`x=4+y=4-3=1`

The solution for this system of equations is x=1 and y=-3.