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Question 145136: Could someone please help me with a few problems?These are Systems of equations,and these are solved by the substitution method.
1)x + y = 15
4x + 3y = 38
2)-3x + y = -4
x - y = 0
Could you please show me step by step on how to work them, because that has helped me so much in the past. I want to thank you so much in advance for all the help you have given me.
Sincerely,
Elle J.
Answer by algebrapro18(249)   (Show Source):
You can put this solution on YOUR website! Lets first review the steps of substitution.
1) Solve one of the two equations for a variable(either x or y).
2) Plug in the thing you just solved for into the other equation and solve for the other variable.
3) Use your number solution to number 2 to solve for the origonal equation.
4) Check your solution. Both numbers must satisfy both equations to be a solution to the system.
1)x + y = 15
4x + 3y = 38
For this first problem lets solve the top equation for y.
x + y = 15 --> Subtract x from both sides
y = -x + 15
Now lets plug in that expression into the second equation and solve for x.
4x + 3y = 38 --> Substitute y = -x + 15 into the equation
4x + 3(-x+15) = 38 --> Distribute the 3
4x + -3x + 45 = 38 --> Combine like terms
x + 45 = 38 --> Solve for x by subtracting 45 from both sides
x = -7
Now Plug x = -7 into the expression we found when we solved the first equation to solve for y.
y = -x + 15 --> Plug x = -7 into the expression
y = -(-7) + 15 --> Simplify and solve for y
y = 22
So as you can see we got the answer x = -7 and y = 22. Now lets check our solution.
x + y = 15 --> Plug in x = -7 and y = 22
-7 + 22 = 15 --> Simplify
15 = 15
4x + 3y = 38 --> Plug in x = -7 and y = 22
4(-7) + 3(22) = 38 --> Complete the multiplication
-28 + 66 = 38 --> Simplify
38 = 38
since both equations checked out we know that our solution of x = -7 and y = 22 worked out.
2)-3x + y = -4
x - y = 0
Here we want to solve the bottom equation for x.
x - y = 0 --> Add y to both sides
x = y
Now substitute that expression into equation 1 and solve for y.
-3x + y = -4 --> Plug y in for x
-3(y) + y = -4 --> combine like terms
-2y = -4 --> Divide both sides by -2
y = 2
Plug y = 2 into the first expression and solve for x.
x = 2
Now we check our solution of x = 2 and y = 2.
-3x + y = -4 --> Plug x = 2 and y = 2 into the equation
-3(2) + 2 = -4 --> complete the multiplication
-6 + 2 = -4 --> Simplify
-4 = -4
x - y = 0 --> Plug x = 2 and y = 2 into the equation
2 - 2 = 0 --> Simplify
0 = 0
Since both equations worked out we know that x = 2 and y =2 is our solution.
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