Question

Solve the following system of linear equations by graphing:- 4x + y = 12- 8x + 2y = 24

Answer 1

Given the following system of linear equations

`\begin{gathered} -4x+y=12\ldots\ldots\text{.}.1 \\ -8x+2y=24\ldots\ldots.2 \end{gathered}`

Let us now make 'y' the subject of the formula in the equations above (writing in slope-intercept form)

From equation 1

`\begin{gathered} -4x+y=12 \\ y=4x+12 \\ \therefore y=4x+12 \end{gathered}`

From equation 2

`\begin{gathered} -8x+2y=24 \\ 2y=8x+24 \\ \text{Divide both sides by 2} \\ (2y)/(2)=(8x)/(2)+(24)/(2) \\ y=4x+12 \\ \therefore y=4x+12 \end{gathered}`

Let us now plot the graph of the equations above

From the above equations written in slope-intercept form, it was observed that the two equations are the same. This means there will be only one graph representing them.

Lastly, since both solutions are the same so therefore the equations have an infinite number of solutions.

The correct answer is Option 3.