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

Substitution Method

The substitution method involves replacing the variables in each equation with the corresponding values from an ordered pair. After substituting, the resulting expressions are evaluated to check if the equations hold true. This method is a straightforward approach to verify if a potential solution is valid.

Verification Process

The verification process entails testing each ordered pair by substituting its values into every equation within the system. If the left-hand side of every equation equals the right-hand side after substitution, then the ordered pair is indeed a solution. If any equation fails this check, the pair is not a solution to the system.

Systems of Linear Equations

A system of linear equations consists of two or more linear equations with common variables. The objective is to find values for these variables that satisfy all equations simultaneously. In problems like these, each equation represents a constraint that must be met, and the intersection of these constraints determines the solution set.

Ordered Pair as a Potential Solution

An ordered pair, usually expressed as (x, y), is a candidate solution to a system of equations. It is considered a true solution if, when its components are substituted into every equation of the system, all equations are satisfied. This is critical in verifying if the pair lies at the intersection of the lines represented by the equations.

Transcript

00:01 All right, so number four, we're going to check to see if part a and b are solutions to the system of linear equations.

00:08 So in order to do that, i am going to take my point and plug in the x and y values and see if it gives me a true statement in my equation.

00:19 So for part a, my x is negative 2 and my y is negative 4.

00:24 So i'm going to check the first equation and see if when i plug in my x and y values, if it's true.

00:30 So 2 times negative 2, which is my x, minus 3 times negative 4, which is my y.

00:38 And we're going to see if that comes out to 8.

00:41 So 2 times negative 2 is negative 4.

00:45 Negative 3 times negative 4 is positive 12.

00:50 So negative 4 plus 12 is 8.

00:56 Therefore, it works for the first equation, which means i need to check my second equation and see if that point is good in my second equation as well.

01:06 It is on my first line and my second line, then that means it is a solution to the system of equations, which would represent the intersection point on a graph.

01:16 So checking my second equation, i have negative 2 minus 2 times negative 4, and we want to see if that is equal to 6.

01:26 So negative 2, and then if i take negative 2 times negative 4, that's going to give me a positive 8.

01:33 So negative 2 plus 8 is 6.

01:36 So since that's true for...

01:37 Both of the equations, that means that negative 2, negative 4, is a solution to the system of linear equations...

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