What point will y+4x=-24 and x=3y-45 intersect

Solve as simultaneous equations or substitute for the x or y value, and then get the other x or y value by substituting.

Substitution method:

y + 4x = -24
x = 3y - 45

Substitute the x into the first equation.

y + 4 (3y-45) = -24

Simplify and solve for y

y + 12y - 180 = -24
13y = -24 + 180
13y = 156
y = 12

Substitute y into one of the equations to find the x value.

x = 3(12) - 45
x = -9

(-9,12) is where the lines intersect.