Given the system of equations:
[tex]\begin{gathered} y=-\frac{1}{3}x+4 \\ y=\frac{2}{3}x+1 \end{gathered}[/tex]Equate the values of y:
[tex]-\frac{1}{3}x+4=\frac{2}{3}x+1[/tex]We solve the equation for x:
[tex]\begin{gathered} 4-1=\frac{2}{3}x+\frac{1}{3}x \\ 3=\frac{2+1}{3}x \\ \frac{3}{3}x=3 \\ x=3 \end{gathered}[/tex]Next, use the value of x=3 to find y:
[tex]\begin{gathered} y=-\frac{1}{3}(3)+4 \\ y=-1+4 \\ y=3 \end{gathered}[/tex]The values of x and y are 3 and 3 respectively.
