The diagram shows the distance between my home, H. and two towns, A and B.
1 answer:
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Answer:
x=−8
y=6=
Step-by-step explanation:
3x+4y=0
5x−3y=−58
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
3x+4y=0,5x−3y=−58
To make 3x and 5x equal, multiply all terms on each side of the first equation by 5 and all terms on each side of the second by 3.
5×3x+5×4y=0,3×5x+3(−3)y=3(−58)
Simplify.
15x+20y=0,15x−9y=−174
Subtract 15x−9y=−174 from 15x+20y=0 by subtracting like terms on each side of the equal sign.
15x−15x+20y+9y=174
Add 15x to −15x. Terms 15x and −15x cancel out, leaving an equation with only one variable that can be solved.
20y+9y=174
Add 20y to 9y.
29y=174
Divide both sides by 29.
y=6
Substitute 6 for y in 5x−3y=−58. Because the resulting equation contains only one variable, you can solve for x directly.
5x−3×6=−58
Multiply −3 times 6.
5x−18=−58
Add 18 to both sides of the equation.
5x=−40
Divide both sides by 5.
x=−8
The system is now solved.
x=−8,y=6
Coordinates are: (-8,6)
Graph:
