Question 268130: I have Three problems on my work sheet that I do not understand how to do. The instructions on the paper says use Substitution to solve each system of equations. My three problems look like this 1. x+2y=13 3x-5y=6 2. x+5y=4 3x+15y=-1 3. x-5y=10 2x-10y=20..... If you could would you please help me figure these problems out. Thank you so much.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! My three problems look like this
Will write a step-by-step solution on the 1st problem
1.
x + 2y = 13
3x -5y = 6
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Choose one equation to be used for substitution, the 1st equation would be simpliest
x + 2y = 13
x = -2y + 13
Now we can substitute (-2y+13) for x in the 2nd equation
3x -5y = 6
Substitute
3(-2y+13) - 5y = 6
Multiply what's inside the brackets
-6y + 39 - 5y = 6
Combine the y's on the left, the numbers on the right:
-6y - 5y = 6 - 39
-11y = -33
The variable (y) has to be positive, multiply both sides by -1
11y = 33
y = 
y = 3
Find x using the substitution equation x = -2y+13, replace y with 3
x = -2(3) + 13
x = -6 + 13
x = +7
Our solution is x=7, y=3
Check this in the 2nd original equation: 3x -5y = 6, replace x & y
3(7) - 5(3) = 6
21 - 15 = 6; confirms our solution
:
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2.
This system does not have a solution, will become apparent as we proceed:
x + 5y = 4
3x +15y= -1
The 1st equation for substitution
x = -5y + 4
Substitute for x in the 2nd equation
3(-5y+4) + 15y = -1
-15y + 12 + 15y = -1
-15y + 15y = -1 - 12
0y = -13, solution undefined, leave it at that
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3.
This system is not solvable either, the two equation are the same
x - 5y = 10
2x- 10y = 20
simplify the 2nd equation, divide by 2
x - 5y = 10
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