Question

Solve the following system of linear equations by graphing:4x + 4y = 2010x + 2y = 18

Answer 1

one solution: (1, 4)

The equations:

y = -x + 5

y = -5x + 9

Step-by-step explanation:
`\begin{gathered} \text{Given equations:} \\ 4x+4y=20\text{ }\ldots(1) \\ 10x+2y=18\text{ }\ldots(2) \end{gathered}`

To plot the graphs, we can assign values to x. The we get the corresponding values of y for each of the equation.

Rewritting the two equations by making y the subject of formula:

`\begin{gathered} 4x+4y=20 \\ \text{divide through by 4:} \\ x\text{ + y = 5} \\ y\text{ = -x + 5} \end{gathered}`
`\begin{gathered} 10x+2y=18 \\ \text{divide through by 2:} \\ 5x\text{ + y = 9} \\ y\text{ = -5x + 9} \end{gathered}`

Plotting the graphs:

The point of intersection of the graphs is the solution.

There is one solution: (1, 4)