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...

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Key Concepts

System of Linear Equations

A system of linear equations consists of two or more linear equations that share the same set of variables. The goal is to find the values of the variables that simultaneously satisfy all the equations in the system. These systems can often be solved by methods such as substitution, elimination, or graphing, and they model situations where multiple conditions must be met at once.

Ordered Pair

An ordered pair is a pair of numbers, typically representing coordinates in the plane or the values assigned to variables in an equation. In the context of systems of equations, each ordered pair represents a potential solution, where the first number corresponds to the first variable and the second number corresponds to the second variable.

Solution Verification

Solution verification involves substituting the proposed ordered pair into each equation of the system to check if all the equations are satisfied. If the substitution results in true statements for every equation in the system, then the ordered pair is considered a valid solution. This approach ensures that the candidate solution meets all the required conditions dictated by the system of equations.

Transcript

00:02 Okay, so we're checking to see if a and b are solutions to the system of linear equations.

00:07 So we are going to take those coordinate points that they give us, and we're going to plug in the x and y values.

00:13 So for part a, the x value is 3, and the y value is 4.

00:17 So i'm going to take those values and replace the variables for the first equation.

00:23 So i'm going to do 3 times my x, which is also 3.

00:26 So 3 times 3 minus my y, which is 4, and see if that gives me 5.

00:30 If it is true for both equations, then it is a solution.

00:35 So three times three is nine, nine minus four is five, which is equal to five.

00:41 So that is a true statement.

00:43 So that means that i need to check my second equation.

00:46 So my second equation is x plus 2y equals 11, replacing my x value with three, my y value with four, and seeing if this is going to give me 11.

01:01 So first i'm going to do multiplication because pemdos or gemdos, whatever you want to say, the order of operations tells me to multiply first.

01:10 So two times four is eight.

01:13 And i'm going to have to add that to the three.

01:15 So three plus eight is 11.

01:17 So since it works for both the first and second equation, that means that three, four is a solution...

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