Solution:
Provided l is perpendicular to m as shown below:
where
[tex]\begin{gathered} m\angle1=(2x+5y)\degree \\ m\angle2=(4x+y)\degree \end{gathered}[/tex]
Since lines l and m are perpendicular, this implies that the measures of angles 1 and 2 are 90 degrees.
Thus,
[tex]\begin{gathered} m\angle1=\text{ 90 degrees} \\ \Rightarrow2x+5y\text{ = 90 ---- equation 1} \\ m\angle2\text{ = 90 degrees} \\ \Rightarrow4x+y=90\text{ ----- equation 2} \\ \end{gathered}[/tex]
To solve for x and y in the above simultaneous equation, we have
[tex]\begin{gathered} From\text{ equation 2, make y the subject of the formula} \\ \Rightarrow y=90-4x\text{ ---- equation 3} \\ Substitute\text{ equation 3 into equation 1,} \\ 2x+5(90-4x)=90 \\ open\text{ parentheses,} \\ 2x+450-20x=90 \\ collect\text{ like terms,} \\ -18x=-360 \\ divide\text{ both sides by the coefficient of x, which is -18} \\ \frac{-18x}{-18}=\frac{-360}{-18} \\ \Rightarrow x=20 \\ Substitute\text{ the value of 20 for x into equation 3,} \\ y=90-4x \\ \Rightarrow y=90-4(20)=10 \end{gathered}[/tex]
Hence, the values of x and y are
[tex]\begin{gathered} x=20 \\ y=10 \end{gathered}[/tex]
