how to do y=(1/3)x-1 5x=9y

Question

Please break down in steps.

Answer 1

two equations, two unknowns can be solved by substitution and elimination or matrix algebra

it also sometimes helps to graph the two equations and see where they intersect

y = (1/3)x -1

3y = x-3

x = 3y+3

5x=9y

5(3y+3) = 9y

15y +15 = 9y

6y = -15

y =-15/6 = -5/2 = -2.5

x =3y+3 = 3(-5/2)+3 = -15/2 +3 = -9/2 = -4.5

graphically, the point of intersection of the two lines is (-4.5, -2.5)

check the answer by plugging that point into each equation, x= -4.5, y =-2.5

y= (1/3)x -1

-2.5 = (1/3)(-4.5) -1 = -1.5 -1 -2.5

5x = 9y

5(-4.5) = 9(-2.5)

-22.5 = -22.5