How to Solve Linear Equations

First, you should know the basic definition of a linear equation. A linear equation stems from the fact that this equation is a straight line in the Cartesian coordinate system. It is of the form Ax+By+C=0 where A, B, and C are real numbers.

Many kinds of linear equations may be derived from the actual equation. First is the linear equation with one variable which is X. For example, 3x+2=11, what is x? To solve, you can apply the Addition Property of Equality (APE) by adding -2 to both sides. You are left with 3x=9, and then by Multiplication Property of Equality (MPE), x=3. This is one of the ways you can solve the equation. The answer x=3 is a straight vertical line passing through (3, 0).

You can also be asked to solve something like this: 5y-7=28, what is y? In this problem, the solution discussed above can also be used. By APE, you can get 5y=35. Also, by MPE, you’ll get y=7 which is a straight horizontal line passing through (0, 7).

In addition, you can be asked to solve a system of linear equations. This will require you to solve the two equations simultaneously to get the values of the two variables. For example, we’re given: x+y=5; and x-y=7. These equations can be solved by either substitution or elimination. Since the y’s in the equations have opposite signs, it is more convenient to use elimination. By adding the two equations, we’re left with 2x=12. As you can see, the y is eliminated in the process of addition. When you finally get the value of x that is when you can substitute it to any of the two equations to get y. The solution set of the two equations would be (6, -1). Also, the point (6, -1) is the point of intersection of these two lines. Moreover, we can conclude that we can solve a system of equations by graphing.

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