ANSWER and EXPLANATION
We want to graph the system of equations and solve them.
To graph a linear equation, we can use two points and then join them.
The two points to be used will be the x and y-intercepts.
To find the x-intercept by finding the value of x when y is 0.
To find the y-intercept by finding the value of y when x is 0.
For the first equation:
[tex]y=-x+2[/tex]
The x-intercept is:
[tex]\begin{gathered} 0=-x+2 \\ \Rightarrow x=2 \end{gathered}[/tex]
The x-intercept is (2, 0)
The y-intercept is:
[tex]\begin{gathered} y=0+2 \\ y=2 \end{gathered}[/tex]
The y-intercept is (0, 2)
For the second equation:
[tex]y=-2x+4[/tex]
The x-intercept is:
[tex]\begin{gathered} 0=-2x+4 \\ 2x=4 \\ x=\frac{4}{2} \\ x=2 \end{gathered}[/tex]
The x-intercept is (2, 0)
The y-intercept is:
[tex]\begin{gathered} y=0+4 \\ y=4 \end{gathered}[/tex]
The y-intercept is (0, 4)
Let us plot the graph of the equations:
The red line represents y = -x + 2
The blue line represents y = -2x + 4
The solution to a system of equations is the point where the lines intersect one another.
Therefore, the solution to the system equations is:
[tex](2,0)[/tex]
