We're done with matrices and are moving onto systems of equations. These are linear equations (so we expect at least two variables) that intersect each other at some point. The point is the answer to our system of equations. With two variables, that means it has to have at least an x answer and a y answer. We display our answer as a coordinate pair (x,y).
To solve using substitution, we have two equations, and expect one variable to be by itself on one side of the equals sign. We substitute that variable, solve for the remaining variable, and find the solution to one variable. Then, once we have that solution, we plug it back into the first equation to get the answer to our other variable.
FOR EXAMPLE:
Solve the system of equations:
y = 2x
6x - 2y = 12
First, we know that y = 2x. That means whenever we see a "y" in the second equation, we can put "2x"
Second equation: 4x - 2(2x) = 12 - substitute
6x - 4x = 12 - multiply
2x = 12 - combine like terms
x = 6 - divide by 2 on both sides to get x = 6
Then go back to the 1st equation y = 2x. Since we know what x is (we just found it, x = 6), we can plug the 6 in for the x and solve for the y:
y = 2x
y = 2(6) - plug in x = 6
y = 12 - multiply to solve
Note that it doesn't matter which variable we find first - the x or the y - because we're going to need both of them to represent the answer. Write your answer as a coordinate pair: (6, 12) since it represents a point on the coordinate plane where your lines intersect.
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