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5.02 Solve Systems with Graphing
1. The Atlanta Hawks scored 92 points in a basketball game. They made a total of 41 baskets. Some baskets were 2-points and some were 3-points. Create a system of equations to represent the problem and find the number of 2- and 3-point baskets made by graphing.
a) name the variables: x is the number of 2-point baskets and y is .
b) set up equation for the number of baskets made:
c) set up equation for the number of points scored:
d) Graph the first equation (number of baskets made. You can do this by hand by picking a value for x (number of 2-point baskets) and solving for y. Let’s pick 2 for x.
x = 2, y =
Therefore, the point (2, ) is on the graph.
Let’s pick another value for x to find a second point on the graph. Let x be 4.
x = 4, y =
Therefore, the point (4, ) is on the graph.
Let’s pick one more value for x. Let x be 6.
x = 6, y =
Therefore, the point (6, ) is on the graph. Graph these three points and sketch the line through them.
e) Graph the second equation. You can do this by hand by picking a value for x (number of 2-point baskets) and solving for y. Let’s pick 1 for x.
x = 1, y =
Therefore, the point (1, ) is on the graph.
Let’s pick another value for x to find a second point on the graph. Let x be 4.
x = 4, y =
Therefore, the point (4, ) is on the graph.
Let’s pick one more value for x. Let x be 7.
x = 7, y =
Therefore, the point (7, ) is on the graph. On the same coordinate plane as before, plot these three points and sketch the line through them.
f) Locate the point were the two graphs cross. This occurs at (,), which means that the number of 2-point baskets (x) scored is , and the number of 3-point baskets (y) scored is .
2. Jenny and her friends are hungry for dessert. They buy $12.25 worth of cookies and ice cream sandwiches. The ice cream sandwiches costs $1.75 each and the cookies cost $0.75 each. If they buy 11 items total, create a system of equations to represent the problem and find the number of cookies and ice cream sandwiches bought by graphing.
a) name the variables: x is the number of ice cream sandwiches and y is .
b) set up equation for the number of items bought:
c) set up equation for the total spent:
d) Graph the first equation. You can do this by hand by picking a value for x (number of ice cream sandwiches) and solving for y. Let’s pick 2 for x.
x = 2, y =
Therefore, the point (2, ) is on the graph.
Let’s pick another value for x to find a second point on the graph. Let x be 4.
x = 4, y =
Therefore, the point (4, ) is on the graph.
Let’s pick one more value for x. Let x be 6.
x = 6, y =
Therefore, the point (6, ) is on the graph. Graph these three points and sketch the line through them.
e) Graph the second equation. You can do this by hand by picking a value for x and solving for y. Let’s pick 1 for x.
x = 1, y =
Therefore, the point (1, ) is on the graph.
Let’s pick another value for x to find a second point on the graph. Let x be 4.
x = 4, y =
Therefore, the point (4, ) is on the graph.
Let’s pick one more value for x. Let x be 7.
x = 7, y =
Therefore, the point (7, ) is on the graph. On the same coordinate plane as before, plot these three points and sketch the line through them.
f) Locate the point were the two graphs cross. This occurs at (,), which means that the number of ice cream sandwiches (x) bought is , and the number of cookies (y) bought is .
3. Solve the system of inequalities by graphing:
a) Prepare to graph by solving each inequality for y.
y
y
Remember to switch the direction of the inequality sign when you divide by a negative number.
b) Graph the two inequalities as if they were equations. Remember, the first equation should have a solid line since it is “greater than or equal to” and the second equation should have a dashed line since it has only “greater than.”
c)Pick a point on either side of each line to determine where to shade. Plug the point into the original inequality. If it is a true statement, shade over the point on the graph above (using the given shapes). If it is a false statement, shade opposite to the point.
Equation 1
Point selected: (,)
Substitution into equation (show your work)
Is this true:
Equation 2
Point selected:(,)
Substitution into equation (show your work)
Is this true:
d) The solution is the overlapping shaded area. Outline it with the purple lines.
4. Solve the system of inequalities by graphing:
a) Prepare to graph by solving each inequality for y.
y
y
b) Graph the two inequalities as if they were equations. Remember to use a dashed line since the inequality signs are “greater than.”
c) Pick a point on either side of each line to determine where to shade. Plug the point into the original inequality. If it is a true statement, shade over the point. If it is a false statement, shade opposite to the point.
Equation 1
Point selected: (,)
Substitution into equation (show your work)
Is this true:
Equation 2
Point selected:(,)
Substitution into equation (show your work)
Is this true:
d) The solution is the overlapping shaded area. Outline it with the purple lines.