1. Put in slope-intercept form: 3x – 4y = Graph the line: y = -1/2 x + 3

 Why would I use the graphing method to solve a system of linear equations?

 2 linear equations graphed on the same coordinate plane  Solution of a System – › An ordered pair, (x,y) where the 2 lines intersect › An ordered pair, (x,y) that makes both equations true

1. Graph each equation on the same coordinate plane. 2. If the lines intersect: The point (ordered pair) where the lines intersect is the solution. 3. Do lines always intersect? 4. What if the lines don’t intersect? Would they have a solution? 5. Do we have a name for lines that will never intersect? What is it? 6. So, if lines are ________, they have ____ solution. parallelno

The coordinates of the point of intersection is the solution 1. Solve the system graphically:

x y We are correct!

The coordinates of the point of intersection is the solution y = - x – 2 y = 2/3 x + 3.

y = - x – 2 y = 2/3 x + 3 xy y = - x – 2 1 = - (-3) – 2 1 = -1(-3) – 2 1 = 3 – 2 1 = 1 y = 2/3 x = 2/3 (-3) = 2/3 (-3/1) = -6/ = = 1 We got it right!

. y = x + 4 y = -x The coordinates of the point of intersection is the solution y = x = y = -x = -(-1) + 2 We did it!

x – y = 5 2x + 2y = The coordinates of the point of intersection is the solution x – y = 5 5 – 0 = 5 2x + 2y = 10 2(5) + 2(5)=10 Dang, we’re good!

Any ideas? Example: Someone says that the solution to the system below is (1, 4). How could we find out if the answer is correct? x - 3y = -5 -2x + 3y = 10

A. (1,4) 1-3(4)= = = -5 *doesn’t work in the 1 st equation, no need to check the 2 nd. Not a solution. B. (-5,0) -5-3(0)= = -5 -2(-5)+3(0)=10 10=10 Solution x - 3y = -5 -2x + 3y = 10 xy x y