What happens if we graph a system of equations and the lines intersect? y = x-1 y = 2x-2

In this lesson you will determine if a system of two linear equations in two variables has one solution by graphing.

Let’s Review Slope Intercept Form of an Equation y = mx + b slopey-intercept

Graphing a linear equation y = 2x + 1 slopey-intercept

y = 2x + 1

A Common Mistake Not having the equation in slope- intercept form 3x + 2y = 4 -3x = -3x 2y = 4 -3x 2 = 2

Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. y = x-1y -2x = 2 +2x = +2x y = 2 + 2x y = 2x + 2

Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. y = x-1 y = 2x-2 Slope: 1, y-intercept: -1 Slope: 2, y-intercept: -2

Let’s Review Core Lesson y = x-1 y = 2x-2 0 = = 0 0 = 2*1-2 0 = 0 (1,0)

Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. -4x + y = 0 y = x+3 +4x = +4x y = 4x

Let’s Review Core Lesson Graph the system of linear equations. Determine their solution. y = 4x y = x+3 Slope: 4, y-intercept: 0 Slope: 1, y-intercept: 3

Let’s Review Core Lesson y = 4x y = x+3 4 = 4*1 4 = 4 4 = = 4 (1,4)

In this lesson you learned to determine if a system of two linear equations in two variables has one solution by graphing.

Let’s Review Guided Practice Find the solution for the system of linear equations y=x and y=2x-4 by graphing.

Let’s Review Guided Practice y=x y=2x-4

Let’s Review Guided Practice Find the solution for the system of linear equations y=2x and y=x+1 by graphing.

Let’s Review Guided Practice y=2x y= x+1

Let’s Review Extension Activities When we solve the systems of equations y=2x and y=x, what is our solution? What does it mean?

Let’s Review Extension Activities How many solutions does the system of equations y=2x+1 and y=x+1 have? Why?

Let’s Review Extension Activities Create a system of linear equations that have only one solution.

Let’s Review Quick Quiz The solution for the system of linear equations y=3x+4 and y=x+2 is? a) (-1,1) b) (1,-1) c)(-1,-1) d) (1,1) The solution for the system of linear equations y=x+6 and y=-2x is? a) (2,-4) b) (-2,4) c) (-2,-4) d) (2,4)