Solve each system by substitution. y=-3 x-20 6 x+2 y=5...

Name: Problem 10, Chapter 5: Beginning and Intermediate Algebra
Uploaded: 2020-06-26T19:58:52-08:00
Duration: 3 min 39 s
Channel: Joshua Fischbach
Description: Solve each system by substitution. y=-3 x-20 6 x+2 y=5

Key Concepts

Equation Simplification

Equation simplification involves combining like terms and performing arithmetic operations to rewrite equations in a simpler form. This is a key step when substituting expressions between equations as it helps in isolating variables and solving for them efficiently.

Substitution Method

The substitution method is a technique used to solve systems of equations where one equation is solved for one variable in terms of the others, and this expression is substituted into the remaining equations. This method reduces the system step by step, eventually isolating each variable, and is particularly useful when one of the equations is already solved for a variable.

System of Linear Equations

A system of linear equations consists of two or more linear equations that share common variables. The goal is to find a set of variable values that satisfy all the equations simultaneously. Such systems often represent real-world scenarios where different conditions or constraints must be met at the same time.

Transcript

00:01 When you're solving a system of equations like this by a substitution, your goal is to either get the x or y by itself in either equation.

00:07 The nice thing is we already have the y by itself right here.

00:12 So it's kind of a nice easy process.

00:14 We can just take that y value and substitute in for y on the other equation.

00:18 So let's do that.

00:20 So the step one here, we don't have to do it.

00:22 We already know that y is equal to negative 3x minus 20.

00:26 So now we're just going to take that value of y and replace it in the other equation.

00:30 Step two.

00:31 So then you get 6 times x plus 2 times the quantity of y, whatever y is, in this case why happens to be negative 3x minus 20, must be equal to 5.

00:48 And now we're going to solve the equation for x.

00:50 So we get 6x plus the quantity of 2 times negative 3x is negative 6x, and 2 times a negative 20 is negative 40, which is distributing.

01:01 And that's equal to 5.

01:04 And then you want to combine your like terms, 6x plus negative 6x is 0.

01:09 So really, this is a 0 minus 40 equals 5.

01:12 And last time i checked, negative 40 doesn't equal 5.

01:15 That's not true.

01:16 So if the variable goes away and you're left with a false statement, this means there's no solution, right? now, what does no solution mean when we're talking about the solution to a system of equations? what it means is that there's no intersection point.

01:30 There's no x and y value where both of these lines have the same solution.

01:35 So these are lines that never intersect, which means that these must be parallel lines.

01:42 Now parallel lines are lines that have the same slope...

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