Question

Consider the system of linear equations given.4x – y = -2y = -3x + 1What is the approximate solution of this system?

Answer 1

Given the system of linear equations, numbered (1) and (2) below

`\begin{gathered} 4x-y=-2\ldots(1) \\ y=-3x+1\ldots(2) \end{gathered}`

Using the substitution method,

Substitute for y into equation

`\begin{gathered} 4x-y=-2 \\ 4x-(-3x+1)=-2 \\ 4x+3x-1=-2 \\ \text{Collect like terms} \\ 7x=-2+1 \\ 7x=-1 \\ x=(-1)/(7) \\ x=-0.14\text{ (two decimal places)} \end{gathered}`

Substitute the value of x into equation (2) to find y

`\begin{gathered} y=-3x+1 \\ y=-3(-0.143)+1 \\ y=0.429+1 \\ y=1.429 \\ y=1.43\text{ (two decimal places)} \end{gathered}`

Hence, the approximate solution of this system is (-0.14, 1.43)