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Question 1171380: Have I correctly solved the 4 problems below using the systems of simultaneous equations, using either the substitution method or the addition method?
Problem 1
x+2y=15
x-2y=-9
2x =6
x=3
3+2y=15
2y=15-3
2y=12
y=6
Problem 2:
x-y=0
7x-3y=24
-3(x-y)=0
-3x+3y=0
7x-3y=24
4x=24
x=6
6-y=0
-y=-6
y=6
Problem 3:
3x-8y=10
x-4y=3
-2(x-4y)=-2(3)
-2x+8y=-6
3x-8y=10
x=4
3(4)-8y=10
12-8y=10
-8y=10-12
-8y=-2
y=1/4
Problem 4:
2x+3y=-5
3x-y=20
3(3x-y)=3(20)
9y-3y=60
9y-3y=60
2x+3y=-5
11x=55
x=5
2(5)+3y=-5
10+3y=-5
3y=-5-10
3y=-15
y=-5
Thank you
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Have I correctly solved the 4 problems below using the systems of simultaneous equations, using either the substitution method or the addition method?
Problem 1
x + 2y = 15
x - 2y = -9
2x = 6
x = 3
3 + 2y = 15
2y = 15-3
2y = 12
y=6
Problem 2:
x - y = 0
7x - 3y = 24
-3(x - y) = 0
-3x + 3y = 0
7x - 3y = 24
4x = 24
x = 6
6 - y = 0
-y = -6
y = 6
Problem 3:
3x - 8y = 10
x - 4y = 3
-2(x - 4y) = -2(3)
-2x + 8y = -6
3x - 8y = 10
x = 4
3(4) - 8y = 10
12 - 8y = 10
-8y = 10-12
-8y = -2
y = 1/4
Problem 4:
2x + 3y = -5
3x - y = 20
3(3x - y) = 3(20)
9y - 3y = 60
9y - 3y = 60
2x + 3y = -5
11x = 55
x = 5
2(5) + 3y = -5
10 + 3y = -5
3y = -5-10
3y = -15
y = -5
Thank you
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Hello, I checked every line in your post.
They ALL are correct.
Very good job. My congratulations (!)
Now, there is another method to check, instead of checking every line.
After completing the solution, you can / (you should) / (you MUST) substitute the obtained numbers (the answer)
into the original equations TO ASSURE that you get valid equalities.
Such checking is INDISPENSABLE and NECESSARY part of the solution.
It is assumed that every student KNOWS about it an MAKES IT after solving each and every such problem.
Well done (!)
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