Question 1171380
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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, &nbsp;I checked every line in your post.


They &nbsp;ALL &nbsp;are correct.


Very good job.  &nbsp;My congratulations &nbsp;(!)



Now, &nbsp;there is another method to check, &nbsp;instead of checking every line.


After completing the solution, &nbsp;you can / (you should) / (you MUST)  &nbsp;substitute the obtained numbers &nbsp;(the answer)

into the original equations &nbsp;TO &nbsp;ASSURE &nbsp;that you get valid equalities.


Such checking is  &nbsp;INDISPENSABLE &nbsp;and &nbsp;NECESSARY &nbsp;part of the solution.

It is assumed that every student &nbsp;KNOWS &nbsp;about it an &nbsp;MAKES &nbsp;IT &nbsp;after solving each and every such problem.



Well done (!)