Question 152702: please help me understand:
explain how to apply substitution in solving a system of equations.
Thank you.
Answer by mangopeeler07(462)   (Show Source):
You can put this solution on YOUR website! Say you have these two equations:
x+3y=26
x=5
Since you have the equation x=5, you can substitute 5 for x in the first equation (since the value of x is directly stated for you, this method is nice and easy to use here).
So plug in 5 for x, like so:
5+3y=26
Now solve for y.
5+3y=26
3y=21
y=7
That is how you can use substitution to find out the other variable. So your solution to this system is:
x=5
y=7
(5,7)
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The same works for y. Say you have this:
3x+y=12
y=3x
This is more flexible. Since y is equal to 3x, you have two choices: 1) plug in y for 3x, or 2) plug in 3x for y. Let's do it both ways:
3x+(3x)=12
6x=12
x=2
or
y+y=12
2y=12
y=6
Since we've done it both ways, we already know both variables, but if we had done it only one way, we would find the other variable by plugging in the variable we know, as in the first example. Like so:
3x+y=12
3(2)+y=12
6+y=12
y=6
or
3x+y=12
3x+6=12
3x=6
x=2
So your solution to this system is:
x=2
y=6
(2,6)
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That is how you can solve a system by using substitution.
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