Write a linear system of equations that can be used to solve these problems. Then, solve to get your final answer. Please help me solve this.
2. The Clippers scored a total of 80 points in a basketball game against the Bulls. The Clippers made a total of 37 two-point and three-point baskets. How many two-point shots did the Clippers make? How many three-point shots did the Clippers make?
total number of two-pointers --- x
number of three-pointers ----- y
take over
I have no clue
To solve this problem, we can set up a system of linear equations.
Let's represent the number of two-point shots made by the Clippers as "x" and the number of three-point shots made as "y."
Based on the information given, we can set up the following equations:
x + y = 37 (Equation 1: The total number of two-point and three-point baskets made is 37.)
2x + 3y = 80 (Equation 2: The total number of points scored is 80.)
We have a system of two equations with two variables. Now, we can solve this system of equations using different methods like substitution, elimination, or graphing.
One way to solve is by substitution:
Step 1: Solve Equation 1 for x:
x = 37 - y
Step 2: Substitute the value of x in Equation 2:
2(37 - y) + 3y = 80
Step 3: Simplify and solve for y:
74 - 2y + 3y = 80
74 + y = 80
y = 80 - 74
y = 6
Step 4: Substitute the value of y in Equation 1:
x + 6 = 37
x = 37 - 6
x = 31
So, the Clippers made 31 two-point shots and 6 three-point shots to score a total of 80 points in the game.