Answer: [tex](6,1.5)[/tex] THE GRAPH IS ATTACHED.
Step-by-step explanation:
The Slope-Intercept form of the equation of a line is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
In this case, you have the first equation:
[tex]y=-\frac{1}{2}x+4\frac{1}{2}[/tex]
You can identify that:
[tex]m=-\frac{1}{2}\\\\b=4\frac{1}{2}[/tex]
If you convert the Mixed number to a Decimal number, you get:
[tex]b=4+0.5=4.5[/tex]
Then, knowing the slope and the y-intercept, you can graph the line.
The second equation is:
[tex]3x-4y=12[/tex]
Solve for "y":
[tex]-4y=-3x+12\\\\y=\frac{3}{4}x-3[/tex]
Knowing that:
[tex]m=\frac{3}{4}\\\\b=-3[/tex]
You can graph the line.
The point of intersection between both lines, is the solution of the system. This is:
[tex](6,1.5)[/tex]
Observe the graph attached.
