Graph the linear system and estimate the solution. Then check the solution algebraically. y

Graph the linear system and estimate the solution. Then...

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Key Concepts

Systems of Linear Equations

A system of linear equations consists of two or more linear equations that are considered simultaneously. The solution to the system is the set of values that satisfy all equations, typically found at the intersection point of their graphs.

Linear Equations

A linear equation is an algebraic statement that creates a straight line when graphed. It generally takes the form y = mx + b, where m represents the slope and b the y-intercept, providing a simple relationship between two variables.

Graphical Method

The graphical method involves plotting the equations on a coordinate plane to visually determine their point of intersection. This intersection represents the solution to the system, offering an estimation that can be checked using algebra.

Algebraic Method (Substitution Method)

The substitution method is an algebraic approach to solving systems of linear equations. This method involves solving one equation for one variable and then substituting that expression into the other equation to find the precise solution.

Solution Verification

Verifying a solution involves substituting the estimated or calculated values back into the original equations to ensure they satisfy all conditions. This step confirms the accuracy of the solution obtained either graphically or algebraically.

Transcript

00:02 Now moving on to this problem, we're actually making our own graph and trying to find the solution or ordered pair solution to our system of linear equations by graphing it ourselves and looking at the point of intersection.

00:15 So i just graphed it on my calculator, but i'm going to draw it out here just so i can make sure you're seeing what i'm seeing.

00:23 So i'll draw our axis lines there.

00:26 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3.

00:32 Now it's important that you label these at least here, negative 3, 3, 3, and now it is implied that each one of these means 1.

00:43 For good practice, you would want to do all of them, but for our sake here, we don't really need to.

00:49 So we had our y equals negative x plus three and y equals x plus one.

00:58 So if we look at our first equation, we know that when we plug in zero for x, it's going to be equal to three.

01:03 So it's going to be here.

01:04 I'll do our first one in red.

01:07 So we have our point there.

01:10 And then if we plug in a positive three for x, we would get our y is equaling to zero because negative three plus three is zero.

01:17 So it would be there.

01:19 So we would have a line looking something like that.

01:23 And then i'll do our other one in blue...

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