7.1 Solving Systems of Equations by Graphing What you’ll learn: To solve a system of linear equations by graphing.

Systems of Linear Equations Two or more equations with 2 or more variables such as 3x+2y=9 x+2y=3 The solution to a system of equations is the intersection of the graphs of the equations. The solution is an ordered pair. (x,y)

3 Possible solutions to a system of equations: One solution (an ordered pair where the graphs intersect) 2. No Solution (Lines don’t intersect because they are parallel which means they have the same slope) Infinitely many solutions (lines are actually the same line so every point on one works for the other, should be the same equations when solved for y) solution

Names for solutions to systems If it has 1 solution the system is called consistent and independent. (Consistent because it has at least one solution and independent because it has exactly 1 solution.) If it has no solution the system is called inconsistent because no ordered pairs satisfy both equations. If it has infinitely many solutions, the system is called consistent and dependent. (consistent because it has at least 1 solution and dependent because it has an infinite number of solutions.)

To solve a system by graphing: Solve each equation for y. Graph by y-intercept and slope. Look for intersection. If they intersect, name the point. If they don’t intersect, write “no solution.” If they are the same line, write “infinitely many.” Check your solution by plugging the ordered pair into both equations to see if it works. If it works for one and not the other, it’s not the solution.

Examples: Solve by graphing y=2x-3 y=-2x+1 Solution: (1,-1) x=-2 y=½x+1 (-2,0) 4x-y=3 2y=8x-6 Solve for y: -y=-4x+3 y=4x-3 for the 1st equ. and y=4x-3 for the 2nd equ Solution: infinitely many y=-⅔x-2 y=-⅔x+1 Solution: No solution

Homework: P. 372 16-34 even