Solving equations with variables on both sides, follow the same steps as multi-step equations. When using the Addition and Subtraction Properties of Equality, one variable will be cancelled out and moved to the other side. It doesn't matter which side of the equal sign that the variable is cancelled on, but generally, I try to keep the variable positive so that I don't have to worry about dealing with a negative sign in my problem.
The goal is always to isolate the variable. In this process, there are a few rules to follow:
1) Distributive Property and combining like terms if necessary.
2) Use inverse operations of addition or subtraction (for variables and constants). This step will get rid of the variable on one side of the equation and we will now see an equation we're used to working with.
3) Use inverse operations of multiplication or division.
Note: If an inequality sign is present, multiplying or dividing by a negative value will flip the inequality sign.
Simultaneous linear equations have one solution, infinite solutions, or no solutions. Although there are various methods to solve simultaneous equations, most linear equations are presented in slope-intercept form (y=mx+b), so the following method would be easiest for these problems.
y = mx +b is the slope intercept form for a linear equation. If we set two linear equations equal to each other, we should have the form:
mx +b = mx +b
where the solution "x" represents the x coordinate where the two lines cross on a coordinate grid. The y coordinate can then be found by substituting the x value back into either linear equation y = mx +b. The coordinate can then be represented as (x,y).
These coordinates can also be found by graphing each linear equation on the same coordinate grid. The one solution is represented by the coordinate where the lines cross. Infinite solutions is when the two lines overlap which means their equations are the same. No solutions is when the two lines do not intersect, meaning the lines are parallel to each other.
The goal is always to isolate the variable. In this process, there are a few rules to follow:
1) Distributive Property and combining like terms if necessary.
2) Use inverse operations of addition or subtraction (for variables and constants). This step will get rid of the variable on one side of the equation and we will now see an equation we're used to working with.
3) Use inverse operations of multiplication or division.
Note: If an inequality sign is present, multiplying or dividing by a negative value will flip the inequality sign.
Simultaneous linear equations have one solution, infinite solutions, or no solutions. Although there are various methods to solve simultaneous equations, most linear equations are presented in slope-intercept form (y=mx+b), so the following method would be easiest for these problems.
y = mx +b is the slope intercept form for a linear equation. If we set two linear equations equal to each other, we should have the form:
mx +b = mx +b
where the solution "x" represents the x coordinate where the two lines cross on a coordinate grid. The y coordinate can then be found by substituting the x value back into either linear equation y = mx +b. The coordinate can then be represented as (x,y).
These coordinates can also be found by graphing each linear equation on the same coordinate grid. The one solution is represented by the coordinate where the lines cross. Infinite solutions is when the two lines overlap which means their equations are the same. No solutions is when the two lines do not intersect, meaning the lines are parallel to each other.
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