Question

Fwam is a high school basketball player. In a particular game, he made some free throws (worth one point each) and some three point shots. Fwam made a total of 10 shots altogether and scored a total of 18 points. Graphically solve a system of equations in order to determine the number of free throws made,

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,
x, and the number of three point shots made,
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y.

Answer 1

• x = 6 (free throws)
• y = 4 (3-pointers)

Explanation:

You want a graphical solution that finds x and y when they total 10 and x+3y is 18.

Graph

The attached graph shows you the solution is ...

(x, y) = (6, 4)

The number of free throws is 6; the number of 3-point shots is 4.

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Additional comment

We like a graphing calculator for solving equations graphically. If you want to graph the equations by hand, you have ...

x +y = 10 . . . . . . x- and y-intercepts are both +10 (shot total equation)

x +3y = 18 . . . . . x-intercept 18; y-intercept 18/3 = 6 (point total equation)

(The intercepts are found by solving the equation with the other variable set to 0. When the equations are in this standard form, the intercepts are the ratio of the constant to the corresponding coefficient.)

The lines cross at (6, 4) in the first quadrant.