Question

Determine the solution to the system of linear equations graphically

Answer 1

We are given a system of two linear equations and our approach is to solve it simultaneously. We can take the elimination, substitution or graphical approach. We will take the elimination approach in this case.

`\begin{gathered} 5x+y=-21\ldots\text{eqn i} \\ 2x+2y=-2\ldots eqn\text{ ii} \\ We\text{ multiply eqn 2 by -}(1)/(2)\text{ to get eqn 3} \\ -x-y=1\ldots(iii) \\ We\text{ add eqns i and }iii\text{to get:} \\ 4x=-20 \\ \text{Divide both sides by 4 to get:} \\ x=-5 \end{gathered}`

To get y, we substitute this value of x into equation i to get:

`\begin{gathered} 5(-5)+y=-21 \\ -25+y=-21 \\ We\text{ add 25 to both sides to get:} \\ y=-21+25=4 \end{gathered}`

x = -5, y = 4

Plotting the equations on a Cartesian graph, we have: