8.1 Solving Systems of Linear Equations by Graphing EQ – HOW CAN YOU SOLVE A SYSTEM OF EQUATIONS BY GRAPHING?

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Presentation transcript:

8.1 Solving Systems of Linear Equations by Graphing EQ – HOW CAN YOU SOLVE A SYSTEM OF EQUATIONS BY GRAPHING?

A. Recall … SLOPE INTERCEPT FORM y = mx + b m = b =

B. Graphing Slope-Intercept Form 1. Graph the y-intercept (0,b) on the y-axis 2. Graph the slope (m) of the line using …. Rise/Run (If there’s whole number turn it into a fraction ALWAYS, ALWAYS, ALWAYS … Y/X

C. Vocab…  System of equations – set of equations that have the same variables  Solution of a system of equations – an ordered pair to show where the system of equations cross each other. (The point where they meet)  The solution MUST work for both equations of the system

D. Rewriting to Slope-Intercept Form From ax + by = c: 1. subtract ax from both sides 2. divide both sides by b 3. Rearrange equation to fit => y = mx + b Example x – 3y = 2 -3x + 9 y = - 6 { x – 3y = 2 -x -3y = 2 – x Y = 1/3x - 2/3 -3x + 9y = x 9y = x y = 1/3x – 2/3

Solving Systems by Graphing  Write the equation in slope-intercept form – GET Y BY ITSELF  Graph each equation  Find the point where the lines intersect  Check: Plug the point into both equations to see if it works for both equations One solution

Pg. 228 … Example B Infinitely Many

Result# of SolutionsGraphWhat does it look like? x=a1Lines Cross a=aInfinite ManySame Line 0Lines don’t cross

Word Problems Standard Form ax + by = c Rewrite both of the equations in slope-intercept form