2. Solve each equation or formula for the variable specified.

3. Math 8H Algebra 1 Glencoe McGraw-Hill JoAnn Evans 5-1 Graphing Systems Of Equations

4. There are different methods available to solve systems of equations. Today you’ll solve systems by graphing………but first you need to know how to recognize a solution when you see one. Two or more linear equations with the same variables form a linear system.

5. ordered pair A solution of a linear system in two variables is an ordered pair that makes each equation a true statement. The ordered pair solution will appear as the point of intersection on the graph. x y The point (-1, -3) is the solution to this system of equations. It is a point common to both lines.

6. To algebraically check the solution for a system of equations, substitute the given values for x and y into each equation. If a true statement is found in both cases, then the given point IS a solution for the system. Check if (0, 4) is a solution of this system: -4x + 3y = 12 -4(0) + 3(4) = 12 0 + 12 = 12 True 3x - 4y = 5 3(0) – 4(4) = 5 0 – 16 ≠ 5 False (0, 4) is NOT a solution to the system. It satisfied only one of the two equations.

7. As we found, the point (0, 4) was a solution for this equation. The point lies on the line. The point (0, 4) was not a solution for this equation. The point doesn’t on the line. The solution for this system of equations is the point of intersection for the two lines. In another lesson you’ll learn how to algebraically find the solution to a system of equations.

8. Check if (2, -1) is a solution of this system: (2, -1) is a solution to the system. It satisfied both of the equations and is the point of intersection for the lines. True

9. Graph the system of equations. Determine the solution. Check the point (5, 2) in both of the original equations to verify that it’s the solution.

10. If the lines you graph aren’t precisely and carefully drawn, it will be very difficult to determine the solution from your graph. Take time to line up your straight edge before you draw the lines!

11. A system of two linear equations can also have no solution or infinitely many solutions. How would a linear system look if it had no solution? x y parallel lines How would one look if it had infinitely many solutions? x y same line

12. Graph the system of equations. Then determine whether the system has one solution, no solution, or infinitely many solutions. If there is one solution, name the solution. The lines are parallel; they have the same slope and different y-intercepts. Parallel lines will never intersect, so there is no solution to the system.

13. There are infinitely many solutions. When the two equations are ready to graph in slope-intercept form, it’s clear that they’re the same line. One solution? No solution? Infinitely many solutions? If there is one solution, name the solution.

14. (6, -3) appears to be the solution for the system. Check the solution in both equations.

15. Bob’s not good at saving money. Today he has $220 in his piggy bank, but every day he takes out $5 for spending money. Ray is better at saving money. Today he has $40 in his piggy bank and plans to add $10 every day to save for a rainy day. In how many days will Bob and Ray’s banks have the same amount of money in them? Let x = # of days until they have the same amount Let y = money in the bank Write two equations in slope-intercept form, one for Bob and one for Ray.

16. 12 3 4 5 6 7 8 9 10 11 12 13 14 # of days 20 40 60 80 100 120 140 160 180 200 220 $ The slope of Bob’s line is -5. Every 4 weeks, he has $20 less. The slope of Ray’s line is 10. Every 2 weeks, he has $20 more. Check the solution in each equation to be sure. (12, 160) After 12 weeks, they will each have $160 in the bank.