Systems of Equations Solution types

Fill in each blank with the correct vocabulary. A system of linear equations is a set of two or more linear equations graphed on the same coordinate plane.The solution to a system of linear equations is the point at which the lines intersect.A system of linear equations has no solution if the lines are parallel, meaning they have the same slope and different y-intercept.A system of linear equations has infinite solutions if the lines are the same, meaning they have the same slope and the same y-intercept. Match each system of linear equations with its solution. No Solution One Solution Infinite Solutions Identifying Solutions Determine if the graph has one solution, no solution, or infinite solutions. in the bubble above the graph type in the solution type. If the graph has one solution in the bubble below the graph type in the ordered pair for the solution; do not put a space between the characters (x,y)If the graph has infinite solutions type (#,#) in the bubble below the graph.If the graph has no solution type an 'X' in the bubble below the graph one solution Infinite solutions no solution one solution Infinite Solutions no solution (2,2) (-1,-2) (#,#) X (#,#) X one solution one solution (-1,-2) (3,-2) no solution X one solution (-1,3) one solution (-4,2) no solution X Solution Types Notes One Solution--The answer will be a single ordered pair, (x,y), where the graph of the lines intersect. you can easily identify if a set of equations has one solution by determining the slope and y-intercept. For systems with one solution the slope and the y-intercept will be different unless they intersect at the y-intercept.Example:Line 1: y = x + 8; Line 2: y = 2x - 2 Line 1:y = -x +7; Line 2: y = 1 + 7No Solution--The lines will never intersect because they are parallel. you can easily identify if a set of equations has no solution by determining the slope and y-intercept. For systems with no solution the slopes of both lines will be the same and the y-intercept will be different.Example:Line 1: y = 2x + 8; Line 2: y = 2x - 2 Infinitely Many Solutions--The lines are actually the same line. you can easily identify if a set of equations has infinite solutions by determining the slope and y-intercept. For systems with infinite solutions the slopes of both lines will be the same and the y-intercept will be the same. If the equations are not written in slope intercept form (y = mx + b) use inverse operations to get y by itself.Example:Line 1: y = 2x + 8; Line 2: -2x + y = 8 Determine Solution Types determine the slope and y-intercept of each equation. Type in the solution type for each equation in the bubble: one solution, no solution, infinite solutions one solution one solution one solution one solution one solution one solution one solution one solution one solution one solution