Solution:
Given the system of equations below:
[tex]\begin{gathered} x+2y=4\text{ ---- equation 1} \\ y=-\frac{1}{2}x+2---\text{ equation 2} \end{gathered}[/tex]
From equation, to graph equation 1, we solve for y for various values of x.
Thus,
[tex]\begin{gathered} when\text{ x =-8,} \\ -8+2y=4 \\ collect\text{ like terms,} \\ 2y=12 \\ divide\text{ both sides by 2,} \\ \frac{2y}{2}=\frac{12}{2} \\ \Rightarrow y=6 \\ \\ when\text{ x = 6,} \\ 6+2y=4 \\ collect\text{ like terms,} \\ 2y=-2 \\ divide\text{ both sides by 2,} \\ \frac{2y}{2}=\frac{-2}{2} \\ \Rightarrow y=-1 \end{gathered}[/tex]
By plotting the values of x and y as points (x, y), we have the graph of equation 1 to be
Similarly, from equation 2, the values of y for various values of x is thus
[tex]\begin{gathered} when\text{ x = 6,} \\ y=-\frac{1}{2}(6)+2=-1 \\ when\text{ x = -8,} \\ y\text{ = -}\frac{1}{2}(-8)+2=6 \end{gathered}[/tex]
By plotting the values of x and y as points (x, y), we have the graph of equation 2 to be
By combining the graphs, we have infinitely many solutions.
