Answer: [tex](2,2)[/tex]
Step-by-step explanation:
1. Substitute [tex]y=0[/tex] into first equation and solve for "x" in order to find the x-intercept of the first line:
[tex]0=-\frac{1}{2}x+3\\\\-3=-\frac{1}{2}x\\\\(-3)(-2)=x\\\\x=6[/tex]
2. Substitute [tex]x=0[/tex] into the first equation and solve for "y" in order to find the y-intercept of the first line:
[tex]y=-\frac{1}{2}(0)+3\\\\y=3[/tex]
Knowing that first line passes through the points [tex](6,0)[/tex] and [tex](0,3)[/tex], you can graph it.
3. Substitute [tex]y=0[/tex] into second equation and solve for "x" in order to find the x-intercept:
[tex]0=2x-2\\\\2=2x\\\\x=1[/tex]
4. Substitute [tex]x=0[/tex] into the second equation and solve for "y" in order to find the y-intercept of the second line:
[tex]y=2(0)-2\\\\y=-2[/tex]
Knowing that second line passes through the points [tex](1,0)[/tex] and [tex](0,-2)[/tex], you can graph it.
The solution of the system of equations is the point of intersection between the lines. Therefore, the solution of this system is:
[tex](2,2)[/tex]
