Question

Solve this system system of equations. Graph and solve the equations

Answer 1

Given:

The system of the linear equations are:

`\begin{gathered} y=-(1)/(2)x+4(1)/(2) \\ 3x-4y=12 \end{gathered}`

Required:

Find the solution of the system by using the graph.

Step-by-step explanation:

The given system is:

`\begin{gathered} y=-(1)/(2)x+4(1)/(2)......(1) \\ 3x-4y=12......(2) \end{gathered}`

Substitute the values of x in equation (1) and find the values of y as:

x=0

`y=4.5`

x=1

`\begin{gathered} y=-(1)/(2)(1)+(9)/(2) \\ y=4 \end{gathered}`

x=- 1

`\begin{gathered} y=-(1)/(2)(-1)+(9)/(2) \\ y=5 \end{gathered}`

x =2

`\begin{gathered} y=-(1)/(2)(2)+(9)/(2) \\ y=3.5 \end{gathered}`

Plot these points on the graph and joined them.

Now substitute the values of x in equation (2) and find the value of y as:

x =0

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

x =1

`\begin{gathered} 3(1)-4y=12 \\ -4y=-9 \\ y=(9)/(4) \\ y=2.2 \end{gathered}`

x=-1

`\begin{gathered} 3(-1)-4y=12 \\ -4y=15 \\ y=-(15)/(4) \\ y=-3.8 \end{gathered}`

Plot these points on the graph and joined them.

We can observe from the graph that the intersection points of the lines are

(6,1.5).

Final Answer:

The solution of the system is (6,1.5).