Question 428586
your equations are:


y = (2/3)*x + 3


and:


3x - 3y = -6


in order to graph these equations, you need to solve for y.


the first one is already solved for y.


the second one is solved for y in the following manner:


3x - 3y = -6
subtract 3x from both sides of the equation to get:
-3y = -3x - 6
divide both sides of the equation by -3 to get:
y = (-3/-3)*x - (6/-3)
simplify this to get:
y = x - (-2)
simplify further to get:
y = x + 2


the 2 equations that you can now graph are:


y = (2/3)x + 3
y = x + 2


the graph of these equations is shown below:


{{{graph(600,600,-5,5,-2,8,(2/3)*x+3,x+2)}}}


the graph shows an intersection at somewhere around x = 3 and y = 5.


you can solve these equations by substitution to see if the answer comes out somewhere near there.


use the original equations of:


y = (2/3)x + 3
3x - 3y = -6


since your first equation has already solved for y, you can use that to substitute for y in the second equation to get:


3x - 3y = -6 becomes 3x - 3*((2/3)x + 3) = -6


simplify by removing parentheses to get:


3x - 3*(2/3)x - 3*3 = -6


simpify further to get:


3x - 2x - 9 = -6


combine like terms to get:


x - 9 = -6


add 9 to both sides of the equation to gert:


x = -6 + 9


simplify further to get:


x = 3


you now have x = 3 and you can substitute for x in either equation to solve for y.


we'll use the first equation.


the first equation is y = (2/3)x + 3


substitute 3 for x to get:


y = (2/3)*3 + 3


simplify to get:


y = 2 + 3 which becomes y = 5


your solution for this set of simultaneous equations is:


x = 3
y = 5


this is confirmed by the graph.