I'll use the substitution method.
-4x + 9y = 9
-4( x ) + 9y = 9
-4( x ) + 9y = 9
-4( 3y-6 ) + 9y = 9 .... x replaced with 3y-6, valid because x = 3y-6
-4( 3y-6 ) + 9y = 9
-4(3y) - 4(-6) + 9y = 9
-12y + 24 + 9y = 9
-3y + 24 = 9
-3y = 9 - 24
-3y = -15
y = -15/(-3)
y = 5
Use that value of y to determine x.
x = 3y-6
x = 3*5-6
x = 15-6
x = 9
The solution as an ordered pair is (x, y) = (9, 5)
Meaning x = 9 and y = 5 pair up together.
Confirmation with a graph.
x = 3y-6 in green
-4x + 9y = 9 in blue
The two lines intersect at (9, 5) to visually confirm the answer.
Desmos and GeoGebra are two graphing tools I recommend. Both are free.
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Another way to check (that doesn't involve a graph).
Plug x = 9 and y = 5 into the first original equation.
Simplify both sides.
The goal is to try to get the same number on both sides.
x = 3y - 6
9 = 3*5 - 6
9 = 15-6
9 = 9 .... confirms the 1st equation
Repeat for the other original equation
-4x + 9y = 9
-4*9 + 9*5 = 9
-36 + 45 = 9
9 = 9 .... confirms the 2nd equation
Both equations are true when x = 9 and y = 5.
The solution has been fully confirmed.
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