Question 80968This question is from textbook Algebra I
: use elimination to solve each system of equations
2m-5n=-6
2m-7n=-14
This question is from textbook Algebra I
Answer by math_tech(1)   (Show Source):
You can put this solution on YOUR website! First you must eliminate one of the variables (m or n in this case) by multiplying one or both equations by the least common multiple on both sides of the equation. Also make sure one of the variables is negative and the other is positive when you add them together.
So, multiply the second equation by -1 to eliminate the m variable.
2m-5n=-6
(-1)(2m-7n)=(-14)(-1)
Now we have:
2m-5n=-6
-2m+7n=14
adding the equations together we get:
0m+2n=8
The 'm' variable is now eliminated, so it just:
2n=8
Solving for n:
n=4
Now, solve for m by substitution n in the first equation:
2m-5(4)=-6
2m-20=-6
Isolate the m variable by adding 20 on both sides:
2m=14
Solve for m:
m=7
Check your answer by substituting m and n values into the second equation:
2(7)-7(4)=-14
14-28=-14
-14=-14
The values satisfy both equations: m=7, n=4
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