SOLUTION: Could you verify if I have correctly used two unknowns and a system of equations to solve the two word problems below? Solve each problem using two unknowns and a system of two

Question 1171488: Could you verify if I have correctly used two unknowns and a system of equations to solve the two word problems below?
Solve each problem using two unknowns and a system of two equations. Also check your work.
Problem 1:
One number is 7 more than another number. The sum of these two numbers is 101. What is the numbers?
x=y+7
x+y= 101
(y+7) + y=101
y+7+y=101
2y=101-7
2y=94
y=47
x=47+7
x=54
Check:
x=47+7=54
54+47=101
Problem 2:
The difference of two numbers is -1. If twice the first number is added to three times the second number, the result is 13. What are the numbers?
x-y=-1
2x+3y=13
3(x-7)=3(-1)
3x-3y=-3
2x+3y=13
5x=10
x=2
2-y=-1
-y=-1-2
-y=-3
y=3
Check:
2-3=-1
2(2)+3(3)=13
4+9=13
13=13
Thank you

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Both are correct.

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