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

step 1 All right, we're checking for solutions on number five. We want to see if part A is a solution t

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

Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations sharing the same set of variables. The solution to the system is the set of variable values that satisfies all equations simultaneously. This concept is fundamental in algebra and is used to find where the lines represented by the equations intersect.

Ordered Pair as a Candidate Solution

An ordered pair represents a potential solution by assigning specific numerical values to each variable in the system. To determine if the ordered pair is indeed a solution, one must check that substituting these values into every equation yields true statements.

Substitution and Verification

The method of substitution involves replacing the variables in the equation with the values from the ordered pair to verify if the equations hold. This process of verification is essential in confirming whether a candidate solution satisfies all equations in the system.

Transcript

00:01 All right, we're checking for solutions on number five.

00:05 We want to see if part a is a solution to the system of linear equations and also part b.

00:10 So for part a, i'm going to take the point negative 3, negative 3, which means both my x and my y value are negative 3.

00:17 And i'm going to see if that point falls on both of my lines.

00:21 Now, the way i do that is by plugging in my values for x and y and seeing if the statement is true.

00:26 So the equation is just a sentence, and we want to see if that sentence is a true statement.

00:32 So my first equation is 2y equals 4x plus 6.

00:36 So where i see y and x, i'm going to replace it with their values of negative 3.

00:45 So starting on the left hand side, i have 2 times negative 3.

00:48 So negative 6 is on the left hand side of my equation.

00:53 So now i have to see if the right hand side is also going to be negative 6.

00:56 So 4 times negative 3 is negative 12 plus 6, which is in fact negative 6.

01:05 So since it works, we have to check the second equation.

01:09 So negative 6 is equal to negative 6.

01:11 Since that's true, that means i need to check the second equation for that point.

01:16 So 2x minus y equals negative 3 is my second equation.

01:20 Once again, i'm plugging in negative 3 for both my x and my y values.

01:29 And seeing if this is a true statement.

01:32 So 2 times negative 3 is negative 6.

01:34 I have a minus negative 3, which is the same as having plus 3.

01:38 So then negative 6 plus 3 is negative 3, which is equal to negative 3.

01:44 So that statement is true.

01:46 So therefore, since both of them are correct, that means that negative 3, negative 3 is a solution.

02:01 All right.

02:02 So checking for part b, part b, the point is 03.

02:07 So my x values are going to become zeros, and my y values are going to become 3.

02:15 So let's check our first equation, 2y equals 4x, plus...

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