Question 1201819
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Answer: <font color=red size=4>(9, 5)</font>
x = 9, y = 5



Work Shown:


I'll use the substitution method.
-4x + 9y = 9
-4( x ) + 9y = 9
-4( <font color=blue size=4>x</font> ) + 9y = 9
-4( <font color=blue size=4>3y-6</font> ) + 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) = <font color=red size=4>(9, 5)</font>
Meaning x = 9 and y = 5 pair up together.


Confirmation with a graph.
{{{
drawing(400,400,-2,12,-2,12,
graph(400,400,-2,12,-2,12,-100,(x+6)/3,(9+4x)/9),
red(
circle(9,5,0.04),
circle(9,5,0.06),
circle(9,5,0.08),
circle(9,5,0.10),
circle(9,5,0.12),
circle(9,5,0.14),
locate(9+0.2,5-0.2,"(9,5)")
),

line(9,0,9,0.125),line(9,0.25,9,0.375),line(9,0.5,9,0.625),line(9,0.75,9,0.875),line(9,1,9,1.125),line(9,1.25,9,1.375),line(9,1.5,9,1.625),line(9,1.75,9,1.875),line(9,2,9,2.125),line(9,2.25,9,2.375),line(9,2.5,9,2.625),line(9,2.75,9,2.875),line(9,3,9,3.125),line(9,3.25,9,3.375),line(9,3.5,9,3.625),line(9,3.75,9,3.875),line(9,4,9,4.125),line(9,4.25,9,4.375),line(9,4.5,9,4.625),line(9,4.75,9,4.875),

line(0,5,0.225,5),line(0.45,5,0.675,5),line(0.9,5,1.125,5),line(1.35,5,1.575,5),line(1.8,5,2.025,5),line(2.25,5,2.475,5),line(2.7,5,2.925,5),line(3.15,5,3.375,5),line(3.6,5,3.825,5),line(4.05,5,4.275,5),line(4.5,5,4.725,5),line(4.95,5,5.175,5),line(5.4,5,5.625,5),line(5.85,5,6.075,5),line(6.3,5,6.525,5),line(6.75,5,6.975,5),line(7.2,5,7.425,5),line(7.65,5,7.875,5),line(8.1,5,8.325,5),line(8.55,5,8.775,5)
)
}}}
x = 3y-6 in green
-4x + 9y = 9 in blue
The two lines intersect at <font color=red size=4>(9, 5)</font> to visually confirm the answer.


Desmos and GeoGebra are two graphing tools I recommend. Both are free.


-----------------------


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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