In the following exercises, solve the systems of equations by substitution. { 5 x+2 y=2

In the following exercises, solve the systems of equations...

Key Concepts

System of Equations

A set of equations with multiple variables that need to be satisfied by the same set of values. They often arise in contexts where multiple relationships between the variables are present, and the goal is to find common solutions that satisfy all the equations simultaneously.

Linear Equations

Equations in which the variables appear to the first power and are not multiplied together. They represent straight-line relationships when graphed and are fundamental in describing many real-life scenarios as well as being the building blocks for more complex algebraic concepts.

Substitution Method

A technique for solving systems of equations by isolating one variable in one equation and substituting the resulting expression into the other equation(s). This method reduces the system to a single equation in one variable, simplifying the process of finding solutions.

Transcript

00:02 So for this problem here, we are given a system of equations and they ask us to solve it using substitution.

00:12 Let's just jump right into it.

00:15 So this bottom equation, the second one, looks very good for us to use for substitution.

00:22 Now, the goal for substitution is to make sure you have a variable by itself with a coefficient of one.

00:33 After you've manipulated one of the two equations, and then whatever you got for that, you pop it into the second one, and you get a value for one variable.

00:48 You'll see it as it goes along.

00:50 So i'm going to take the first one.

00:52 I'm sorry, i'm going to take the second equation, negative 3x minus y equals zero, and i'm going to get y by itself.

01:04 So i'm going to add y to both sides.

01:16 So these two ys will cancel out and we'll have negative 3x is equal to y.

01:26 Now, since we use the second equation for that, we're going to pop that into the first equation.

01:31 So we're going to do 5x plus 2.

01:36 Now wherever we see a y, we're going to put a negative 3x.

01:40 We're going to put negative 3x equals 2.

01:47 Right here we're going to do some distributive property.

01:50 So we're going to do 5x.

01:54 Positive 2 times negative 3 is negative 6x is equal to 2.