Answer: (x, y) = (-12, 3)
This means x = -12 and y = 3 pair up together to form the solution.
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Work Shown
1/2 = 0.5
0.5x + 6y = 12
0.5x + 6(x+15) = 12 .... plug in y = x+15
0.5x+6x+90 = 12
6.5x + 90 = 12
6.5x = 12-90
6.5x = -78
x = -78/(6.5)
x = -12
Then,
y = x+15
y = -12+15
y = 3
The solution as an ordered pair is (x, y) = (-12, 3)
That is the shorthand way to indicate x = -12 and y = 3 pair up together to form the full solution.
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Check:
Plug x = -12 and y = 3 into the first equation. Simplify both sides.
0.5x + 6y = 12
0.5*(-12) + 6*3 = 12
-6 + 18 = 12
12 = 12
We reached a true statement, which confirms the first equation is true when x = -12 and y = 3.
Repeat for the second equation.
y = x+15
-3 = -12+15
-3 = -3
This equation is true as well. Both equations are confirmed.
A visual way to confirm the answer is to graph the original equations on the same xy grid. The two lines intersect at (-12, 3). See the diagram below. I used GeoGebra to make the graph. Desmos is another option.