C HAPTER 7 S ECTIONS 1-3 R EVIEW & 6-6. 7-1 S OLVING S YSTEMS BY G RAPHING Rewrite each equation so that it reads y = mx + b Graph each line individually.

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Presentation transcript:

C HAPTER 7 S ECTIONS 1-3 R EVIEW & 6-6

7-1 S OLVING S YSTEMS BY G RAPHING Rewrite each equation so that it reads y = mx + b Graph each line individually on the same coordinate plane. Note where the two line intersect, that is the solution to the system of equations. If the two lines do not intersect (they have the same slope & different y-intersects) the lines are parallel they have NO SOLUTION. If the lines are the same line (same slope & same y-intercept) they have INFINATELY MANY SOLUTIONS Practice problems Page all, 15-22all, all

6-6 P ARALLEL & P ERPENDICULAR L INES Parallel lines has the same slopes and different y- intercepts. If you are given a line an a set of point and asked to find a line parallel to that line that contains those point in slope-intercept form, you must put it in point- slope form first. Then rearrange it into slope-incept form. The product of the slope of perpendicular lines equals -1. If you are given a line an a set of point and asked to find a line perpendicular to that line that contains those point in slope-intercept form, you must put it in point-slope form first. Then rearrange it into slope- incept form. Remember that the slope of a line perpendicular is the opposite reciprocal. Practice problems Page all, 32-40all

7-2 S OLVING S YSTEMS U SING S UBSTITUTION You can only use this method if you have a variable with a coefficient of one. You only need to rearrange one of the equations so that it equals the variable with the coefficient of one. If both equations equal the same variable then set them equal to each other and solve for that variable. You must solve for both variables. Make sure you read the directions, if they read check your solutions then put your x & y values back into your original equations and make sure they work. Practice problems Page all, 19-21all, all, 34-39all

7-3 S OLVING S YSTEMS U SING E LIMINATION If you have two variables with the same coefficient and different signs then add them. If you have two variables with the same coefficient and the same sign then subtract them. If you have two variables with nothing in common then find the LCD and multiply the entire equation by the LCD and eliminate one of the variables and solve for the other one. Practice problems Page all, 9-14all, all, 33-38all