You have to use substitution to solve for y or elimination to solve for x.
What is the answer to 6x+2y=10 and 2x-2y=-2?
- Posted:
- 3+ months ago by afrederi3...
- Topics:
- math, answer
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Answers (3)
You have two lines. Looks like this: www.wolframalpha.com/input/?i=plot+6x%2B2y%3D10,+2x-2y%3D-2
Where they cross, the values of x and y satisfy both equations simultaneously, so it is called a simultaneous system. There are two ways to find that point. Substitution is when you solve one equation for one variable and substitute that into the other equation.
2x - 2y = -2
6x + 2y = 10 We'll start with this one.
2y = 10 - 6x
y = 5 - 3x Now substitute this for y in the other equation.
2x - 2y = -2
2x - 2(5 - 3x) = -2
2x - 10 + 6x = -2
8x = 8
x = 1 Put this in either equation to find y.
y = 2
Elimination is when you add the equations in a way to eliminate one variable. Otherwise the process is the same.
2x - 2y = -2
6x + 2y = 10
---------------- ADD
8x ...... = 8
x = 1 <-- SAME ANSWER
By elimination method:
6x+2y=10 (equation 1)
2x-2y=-2 (equation 2)
------------------------------ add the two equations to eliminate y
8x + 0 = 8
8x = 8
divide both sides by 8
8x/8 = 8/8
x = 1
substitute 1 for x in any of the original equations
6x+2y=10
6(1)+2y=10
6 + 2y = 10
subtract 6 from both sides
6 - 6 + 2y = 10 - 6
2y = 4
divide both sides by 2
2y/2 = 4/2
y = 2
6x + 2y = 10
+
2x - 2y = -2
-----------------
8x = 8
x=1
you can do it with y as well where you have the x's eliminate each other, but make sure each time you go and see that that answer does work. I know of times where you get the answer and it is correct, but not feasible.