Landon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Landon scored a total of 24 points and made 2 more two point shots than three point shots. Graphically solve a system of equations in order to determine the number of two point shots made, x, and the number of three point shots made, y.

Question

Landon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Landon scored a total of 24 points and made 2 more two point shots than three point shots. Graphically solve a system of equations in order to determine the number of two point shots made,  x, and the number of three point shots made,  y.

Bytelearn · Accepted Answer

Define variables: Let's define two variables: x for the number of two point shots and y for the number of three point shots. We can set up two equations based on the information given. The first equation comes from the total points scored, which is 24. Since two point shots are worth 2 points each and three point shots are worth 3 points each, the equation is: 2x + 3y = 24Set up equations: The second equation comes from the information that Landon made 2 more two point shots than three point shots. This can be written as: x = y + 2Solve first equation: Now we have a system of two equations: 1) 2x + 3y = 24 2) x = y + 2 We can use substitution or elimination to solve this system. Let's use substitution since the second equation is already solved for x. We'll substitute y + 2 for x in the first equation. 2(y + 2) + 3y = 24Combine like terms: Now let's distribute the 2 and combine like terms: 2y + 4 + 3y = 24 5y + 4 = 24Isolate y term: Next, we'll subtract 4 from both sides to isolate the term with y: 5y + 4 - 4 = 24 - 4 5y = 20Solve for y: Now we'll divide both sides by 5 to solve for y: 5y / 5 = 20 / 5 y = 4Substitute back for x: Now that we have the value for y, we can substitute it back into the second equation to find x: x = y + 2 x = 4 + 2 x = 6Check solution: We have found the values for x and y. Landon made 6 two point shots and 4 three point shots. To check our work, we can plug these values back into the original equations to ensure they satisfy both: 2x + 3y = 24 2(6) + 3(4) = 24 12 + 12 = 24 24 = 24

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