Determine whether each ordered pair is a solution of the system of linear equations. See Example

Determine whether each ordered pair is a solution of the...

Key Concepts

System of Linear Equations

A system of linear equations is a collection of two or more linear equations involving the same set of variables. The solution to the system is the set of values for the variables that satisfy every equation simultaneously. This concept is fundamental in algebra and is used to model problems where different conditions need to be met concurrently.

Verification of Solutions

Verifying whether an ordered pair is a solution entails checking if the pair satisfies every equation in the system when substituted into them. This process confirms the accuracy of the solution for the system, ensuring that all constraints represented by the equations are met.

Substitution Method

The substitution method is a technique used to verify a potential solution by replacing the variables in each equation with the corresponding values from the ordered pair. If the resulting expressions hold true (i.e., both sides of the equations are equal), the ordered pair is considered a valid solution for that equation and, collectively, for the system.

Transcript

00:01 Alright, in number six, we're checking to see if parts a and b are a solution to the system of linear equations.

00:07 So in order to do that, we want to see if these points fall on both of the lines.

00:12 So when i plug in my x and my y values, they should both be true for it to be a solution to the system of equations.

00:20 So starting with a, my point is negative 4, so anywhere i see x, i'm going to put in a negative 4.

00:27 And anywhere i see the variable y, i'm going to put in a 0.

00:30 So i'm going to start with my first equation x plus 5y equals negative 4.

00:39 So that's going to be negative 4 plus 5 times 0 equals negative 4.

00:44 So this is going to be negative 4 plus 0 because 5 times 0 is just 0, which tells me that my equation or my statement is true because negative 4 is equal to negative 4.

00:56 So that leads me into my second equation, which i must also check.

01:01 If it works for both equations, then it is a solution.

01:05 So i'm going to do negative 2 times my x of negative 4.

01:10 I'm going to do 10 times my y of 0 plus 8.

01:14 So on the left hand side, i have negative 2 times negative 4, which is positive 8.

01:19 And on the right hand side, i have 10 times 0, which is 0 plus 8, which is also positive 8.

01:26 So since both of the equations work for that point, that means that negative 4 is a solution.

01:34 Which means it's where they would cross.

01:38 If you graph them, a point where they would cross or both lines would be on that point.

01:45 All right.

01:45 So i'm going to check part b.

01:47 Same way i checked part a.

01:49 So 6 negative 2, where x is 6 and y is negative 2, we're going to plug that into my first equation and see if it's true.

02:01 So 6 plus 5 times negative 2 will it give me negative 4? i have to use the order of operation.

02:10 So i'm going to start with 5 times negative 2, which is negative 10.

02:15 So i'm going to have 6 minus 10, which is negative 4...

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