Given:
The system of the linear equations are:
[tex]\begin{gathered} y=-\frac{1}{2}x+4\frac{1}{2} \\ 3x-4y=12 \end{gathered}[/tex]
Required:
Find the solution of the system by using the graph.
Explanation:
The given system is:
[tex]\begin{gathered} y=-\frac{1}{2}x+4\frac{1}{2}......(1) \\ 3x-4y=12......(2) \end{gathered}[/tex]
Substitute the values of x in equation (1) and find the values of y as:
x=0
[tex]y=4.5[/tex]
x=1
[tex]\begin{gathered} y=-\frac{1}{2}(1)+\frac{9}{2} \\ y=4 \end{gathered}[/tex]
x=- 1
[tex]\begin{gathered} y=-\frac{1}{2}(-1)+\frac{9}{2} \\ y=5 \end{gathered}[/tex]
x =2
[tex]\begin{gathered} y=-\frac{1}{2}(2)+\frac{9}{2} \\ y=3.5 \end{gathered}[/tex]
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
[tex]\begin{gathered} 3(0)-4y=12_ \\ y=-3 \end{gathered}[/tex]
x =1
[tex]\begin{gathered} 3(1)-4y=12 \\ -4y=-9 \\ y=\frac{9}{4} \\ y=2.2 \end{gathered}[/tex]
x=-1
[tex]\begin{gathered} 3(-1)-4y=12 \\ -4y=15 \\ y=-\frac{15}{4} \\ y=-3.8 \end{gathered}[/tex]
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).
