Solve by the addition method. y =2 x-3 3 x+4 y =-1 ...

Name: Problem 32, Chapter 13: Prealgebra and Introductory Algebra
Uploaded: 2020-06-23T16:20:03-08:00
Duration: 3 min 14 s
Channel: Cullen Miller
Description: Solve by the addition method. y =2 x-3 3 x+4 y =-1

Key Concepts

Addition (Elimination) Method

The addition method, also known as the elimination method, is an approach used to solve systems of linear equations by removing one of the variables. This is achieved by appropriately multiplying the equations, if necessary, so that the coefficients of a chosen variable are opposites. When the equations are added or subtracted, the chosen variable cancels out, leaving an equation with a single variable that can be solved. The found value is then substituted back into one of the original equations to determine the other variable(s).

System of Linear Equations

A system of linear equations consists of two or more linear equations that share common variables. The goal when solving such a system is to find values for the variables that satisfy all the given equations simultaneously. These systems can have one unique solution, infinitely many solutions, or no solution at all.

Transcript

00:01 Hello, hope you're doing well.

00:02 So we've got our system of equations here that we're going to solve using the addition method.

00:06 But the first thing you may notice is that our common terms are not lined up.

00:09 So we need to get those lined up first.

00:12 So i'm going to rewrite this first equation here, and we're going to subtract 2x from both sides of our equation, and we're left with minus 2x plus y is equal to minus 3.

00:24 Then we can just rewrite our second equation down here.

00:30 And now we've got everything lined up properly.

00:33 So now we need to try and eliminate one of our variables.

00:37 So we're going to try and eliminate our variable x.

00:40 So to do that, we're going to multiply this first equation, both sides of our equation by three.

00:44 Then we're going to multiply both sides of the second equation by two.

00:48 So for our first equation, distributing this three, we've got three times minus 2x is going to give us minus 6x.

00:56 We've got three times y.

00:58 It's going to give us plus 3y.

01:01 We've got 3 times minus 3, which is going to be equal to minus 9.

01:06 And moving on to our second equation, distributing the 2, we've got 2 times 3x, which gives us 6x.

01:12 We've got 2 times 4y, which gives us plus 8y.