Solve each system using substitution. x-7=y 2 x-y=41 |...

Name: Problem 51, Chapter 6: Algebra 1 Common Core
Uploaded: 2020-03-31T02:16:07-08:00
Duration: 2 min 35 s
Channel: Shawn Gedert
Description: Solve each system using substitution. x-7=y 2 x-y=41

Key Concepts

Substitution Method

The substitution method is a strategy used to solve systems of equations by expressing one variable in terms of another using one of the equations, and then replacing that expression in the other equation. This reduces the system to a single equation with one variable, making it easier to solve before back-substituting to find the remaining unknowns.

Systems of Linear Equations

This concept involves sets of equations with multiple variables that are solved together because they have common solutions. Each equation in the system represents a constraint, and the solution is the set of variable values that makes all equations true simultaneously. In algebra, solving these systems allows us to find points of intersection between lines or planes.

Linear Equations

A linear equation is an algebraic expression where the highest power of the variable is one. Such equations graph as straight lines on the coordinate plane. Understanding linear equations is fundamental because they form the building blocks for systems of equations and many applications in algebra.

Transcript

0:00 Hello.

00:02 This is a linear systems problem that we are going to solve using the substitution method.

00:07 So as i look at my top equation here, it's actually already solved for y.

00:15 So that means that if i take this x minus 7 right here, i'm going to make this a little smaller.

00:23 If i take this x minus 7 right here and i substitute that in for y, i'm going to be able to get one equation with one variable x that i can solve and then that'll help me to solve this problem so if i go two times x subtract now you got to be a little careful on this one because i'm going to put that whole thing in parentheses for why because we're subtracting a quantity and that always makes things a little more interesting so it's going to look like this okay um we this subtraction outside of quantity to get rid of these parentheses, what we can do is multiply everything inside this parentheses by a negative one.

01:06 A shortcut to that is changing everything on the inside to the opposite.

01:12 But what happens is we end up with 2x minus 1x and then plus 7 equals 41.

01:23 And now we have, excuse me, and now we have an equation that we can simplify.

01:30 So 2x minus 1x is 1x plus 7 equals 41.

01:35 And then i'm going to subtract 7 on both sides.

01:38 And so 41 subtract 7 is going to be 34.

01:43 So that's going to be the x coordinate that makes this work.

01:46 And then i'm going to substitute this back into my top equation.

01:51 So x minus 7 equals y...