Unit 3 Jump Start - Solving Systems of Linear Equations

Unit 3 Jump Start - Solving Systems of Linear Equations

Recall what it means to be a "solution" to an equation

The solution to an equation is the value of the variable that makes the equation true

In this unit we are going to be solving systems of linear equations

A system of linear equations is a set of two or more equations containing two or more variables

So can a system of equations have a solution?

Yes!

Solution to a system of equations

The set of all points that satisfy each equation. In most cases this is one point that makes both equations true.

The first method we will use to solve systems is graphing.

We will graph both equations on the same coordinate plane.

Let's practice

Multiple Choice

Graph the linear equation $y=-2x+3$  

Multiple Choice

Write the equation $x+2y=4$  in slope-intercept form

•  $2y=-x+4$  

•  $y=\frac{1}{2}x-4$  

•  $y=2x+4$  

•  $y=-\frac{1}{2}x+4$  

Open Ended

Based on the tables of values in the photo, what is the solution to this system of linear equations?

Both tables contain the point  $\left(1,\ 5\right)$  

So that x and y solves both equations. That makes it the solution to the system.

A system of equations can have:

• 1 solution: The lines intersect

• 0 solutions: The lines are parallel

• Infinitely many solutions: Both equations are the same line, so they have all points in common