SOLUTION: Use the substitution method to solve the linear system given. Express the answer as an ordered pair of the form (x,y) x + y = 5 2x + y = 6

Question 254478: Use the substitution method to solve the linear system given. Express
the answer as an ordered pair of the form (x,y)
x + y = 5
2x + y = 6
Found 2 solutions by unlockmath, PRMath:
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
There's a couple ways to solve this. Let's take the first equation:
x + y = 5
2x + y = 6
And rewrite it as
y = 5 - x
Now plug this into the second equation to give us:
2x +(5-x)=6 Now we can solve x
x+5=6 Subtract 5 from both sides will give us:
x=1 Now we can go back to the original equations and find y
1 + y = 5 Subtract 1 from both sides:
y =4
Plug in y=4 and x=1 into both equations and it will work out good!
RJ
Check out a new math book at:
www.math-unlock.com

Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
x + y = 5
2x + y = 6

What if you took the first equation and solved for "X". Let's do that. Let's take the first equation and solve for "X".

x + y = 5(first equation)
x = 5 - y (subtract y from both sides to isolate/solve for "X")

Now that you know x = 5 - y, you can SUBSTITUTE 5 - y into the 2nd equation, where the "X" variable is.

2x + y = 6 (2nd original equation)
2(5 - y) + y = 6 (see where "X" was replaced with 5 - y)?
10 - 2y + y = 6 (distribute the 2 and multiply 2 times 5 and then 2 times -y)
10 - 1y = 6 (combine like terms: -2y + y = -1y)
-1y = 6 - 10 (subtract 10 from both sides to isolate the "Y")
-1y = -4 (6 - 10 = -4)
y = 4 (divide both sides by -1 to isolate the y).

Now you know that y = 4. Let's put that info into our first equation:

x + y = 5 (original equation)
x + 4 = 5 (see where "Y" was replaced with the number 4)?
x = 5 - 4 (subtract 4 on both sides to isolate the "X")
x = 1

Now you know that x = 1.

The ordered pair then, which is in this format (x, y) is (1, 4).

Does this work in the answer? Let's "plug" in the x and y info into the original equations:

x + y = 5 (first original equation)
1 + 4 = 5 (equation with x and y info "plugged" in)
5 = 5 YES the ordered pair (1, 4) fits in this equation and makes it true.

2x + y = 6 (second original equation)
2(1) + 4 = 6 (equation with x and y info "plugged" in)
2 + 4 = 6
6 = 6 YES the ordered pair (1,4) fits into this equation as well and makes it true.

I hope this is helpful to you. :-)
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