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Mathematical substitution is the process of using one equation to solve for multiple variables. For example:
Equation 1: x + y = 4
Equation 2: 2x + y = 16
Using equation 1, solve for y:
y = 4 - x <-- Plug this into equation 2. This is substitution because you are replacing y in equation 2 with what y is equal to in equation 1.
2x + y = 16 ----> 2x + (4 - x) = 16
Now you can solve for x: x + 4 = 16; x = 12
You can then substitute the value of x back into the equation that is solved for y:
y = 4 - 12; y = -8
Check both equations:
Equation 1: -8 + 12 = 4; 4 = 4 (Correct)
Equation 2: 2(12) + (-8) = 16; 24 - 8 = 16; 16 = 16 (Correct)
We have successfully used substitution to solve for two different variables, x and y.
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Can substitution in math be used to find the exact solution of a system of equations?
yes
How do you check a solution to an equation?
By substitution.
Why is graphing easier than using elimination or substitution?
Graphing is not necessarily easier than elimination or substitution. If you are good at drawing graphs, and do not like algebra, then graphing is easier. However, elimination and substitution are much faster, and graphing can often get awkward when working with more complicated formulae.
When solving by the substitution method what happens when one variable cancels out?
That's exactly the purpose of the substitution method ... to get an equation with one less variable. When you have it, you solve it for the variable that's left.
To solve a three variable system of equations you can use a combination of the elimination and substitution methods?
True. To solve a three variable system of equations you can use a combination of the elimination and substitution methods.
