How Do You Solve Systems Of Linear Equations By Substitution?

Solving systems of linear equations is a skill not only taught in basic algebra but also tested on the ACT and SAT exams and even job application tests."Solving a system" is fancy language for finding the values of x and y that will make two equations true. "Substitution" means isolating one of the variables, x or y, in one of the equations, then "substituting" it, or plugging it in, to the other. Understand that solving a "system" means you are working with two equations.

An "equation" means that an equals sign separates two sides of a number sentence. Each equation will have two "variables," or unknown values. Usually, variables are identified with the letters x and y, though any letters can be used.

For this example, we will work with the following two equations:2x + y = 812 + 3x = 10y + 1 Choose one of the equations to start with. The first step is isolating either x or y. Isolate means to set it on one side of the equals sign.

Let's choose the first equation: 2x + y = 8. Since y ... more.

One common type of problem in algebra is to find the intersection of two linear equations to find their solution. Of graphing, elimination, and substitution, substitution is the most reliable and versatile technique. This tutorial will show you how to solve a system of equations by substitution.

Solve one equation for a single variable. This sounds hard, but is pretty easy. Let's use the system of equations X + Y = 2 2X -Y = 4 as an example.

I am going to solve the first equation for X to get X = 2 - Y. This expression shows that X is equivalent to 2-Y, and I can use this to plug it into the second equation. Plug the solved equation into the other equation.

Here we plug in (2-Y) wherever we see an X in the bottom equation 2(2-Y) - Y = 4 4 - 2Y - Y = 4 -3Y = 0 Y = 0 Now we know what Y is! Plug your value into your solved equation from step one to find the other variable. X = 2-Y X = 2-0 X =2 So our solution for this system of equations is X=2, Y=0, or the coordinate (2,0) which is the ... more.

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