This is the best way to be given a system of equations to solve.
Each equation is the equation of a straight line and the solution represents the point where they intersect.
The fact that they both have #y# as the subject makes them very easy to solve.
We have#color(blue)(y = 4x+24)" and "color(red)(y = x+9)#
Consider that if #color(white)(xxxxxx)color(blue)(y)=color(red)(y)#
it follows that #" "color(blue)( 4x+24) = color(red)(x+9)#
#color(white)(xxxxxxxxxxxx)4x-x = 9-24#
#color(white)(xxxxxxxxxxxx)3x=-15#
#color(white)(xxxxxxxxxxxxx)x = -5#
Once you have a value for #x#. there are now 2 ways to calculate a value for y. Use one equation to find #y#,and the other to check the answer.
#y = 4x+24 " "rarr y = 4(-5)+24 = -20+24 = 4#
#y = x+9 " " rarry = -5 +9 = 4#
#x =-5 and y = 4#
