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Question 430110: Hello there. Thank yall for all that you do. I am having a little difficulty with these three problems. Any asistance would be greatly appreciated. Thank you for your time.
using the substitution method
9m+n=10 and m-5n=42
8x-7y=-41 and 4x+43=y
5x+6y=-29 and -8+y=57
(type an ordered pair)
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 9m+n=10_m-5n=42
Since 9m does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 9m from both sides.
n=-9m+10_m-5n=42
Replace all occurrences of n with the solution found by solving the last equation for n. In this case, the value substituted is -9m+10.
n=-9m+10_m-5(-9m+10)=42
Multiply -5 by each term inside the parentheses.
n=-9m+10_m+45m-50=42
Since m and 45m are like terms, add 45m to m to get 46m.
n=-9m+10_46m-50=42
Since -50 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 50 to both sides.
n=-9m+10_46m=50+42
Add 42 to 50 to get 92.
n=-9m+10_46m=92
Divide each term in the equation by 46.
n=-9m+10_(46m)/(46)=(92)/(46)
Simplify the left-hand side of the equation by canceling the common factors.
n=-9m+10_m=(92)/(46)
Simplify the right-hand side of the equation by simplifying each term.
n=-9m+10_m=2
Replace all occurrences of m with the solution found by solving the last equation for m. In this case, the value substituted is 2.
n=-9(2)+10_m=2
Multiply -9 by each term inside the parentheses.
n=-18+10_m=2
Add 10 to -18 to get -8.
n=-8_m=2
This is the solution to the system of equations.
n=-8_m=2
8x-7y=-41_4x+43=y
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
8x-7y=-41_y=4x+43
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 4x+43.
8x-7(4x+43)=-41_y=4x+43
Multiply -7 by each term inside the parentheses.
8x-28x-301=-41_y=4x+43
Since 8x and -28x are like terms, add -28x to 8x to get -20x.
-20x-301=-41_y=4x+43
Since -301 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 301 to both sides.
-20x=301-41_y=4x+43
Subtract 41 from 301 to get 260.
-20x=260_y=4x+43
Divide each term in the equation by -20.
-(20x)/(-20)=(260)/(-20)_y=4x+43
Simplify the left-hand side of the equation by canceling the common factors.
x=(260)/(-20)_y=4x+43
Simplify the right-hand side of the equation by simplifying each term.
x=-13_y=4x+43
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -13.
x=-13_y=4(-13)+43
Multiply 4 by each term inside the parentheses.
x=-13_y=-52+43
Add 43 to -52 to get -9.
x=-13_y=-9
This is the solution to the system of equations.
x=-13_y=-9
5x+6y=-29_-8+y=57
Since -8 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 8 to both sides.
5x+6y=-29_y=8+57
Add 57 to 8 to get 65.
5x+6y=-29_y=65
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 65.
5x+6(65)=-29_y=65
Multiply 6 by each term inside the parentheses.
5x+390=-29_y=65
Since 390 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 390 from both sides.
5x=-390-29_y=65
Subtract 29 from -390 to get -419.
5x=-419_y=65
Divide each term in the equation by 5.
(5x)/(5)=-(419)/(5)_y=65
Simplify the left-hand side of the equation by canceling the common factors.
x=-(419)/(5)_y=65
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -(419)/(5).
x=-(419)/(5)_y=65
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