Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for both variables.
In a basketball game, Will scored 26 points, consisting only of three-point shots and two-point shots. He made a total of 11 shots. How many shots of each type did he make?
first, represent the unknown using variables:
let x = number of 2-point shots
let y = number of 3-point shots
then set-up the equations. for the first statement, total score is 26, so:
2x + 3y = 26
for the second statement, total number of shots is 11, so:
x + y = 11
using substitution:
for the 2nd equation, x + y = 11, express one of the variables in terms of the other,, in this case, i will use x:
x + y = 11 *transpose all terms not containing x
x = 11 - y *when transposing, the sign of the term transposed would be the opposite
then substitute to the 1st equation:
2x + 3y = 26
2(11 - y) + 3y = 26
22 - 2y + 3y = 26
22 + y = 26
y = 26-22 = 4
substituting the value obtained for y on either equations: (in this case, substitute to 1st equation)
x + y = 11
x + 4 = 11
x = 7
therefore,,
x = 7 two-point shots, and
y = 4 three-point shots
so there,, =)
4\x+@=3
4\x+2=3
To solve this problem, we need to translate the information given into a pair of linear equations and then solve them using either elimination or substitution. Let's proceed with substitution.
Let's represent the number of three-point shots as 'x' and the number of two-point shots as 'y'.
We know that Will scored a total of 26 points. Since each three-point shot is worth 3 points and each two-point shot is worth 2 points, we can write the equation:
3x + 2y = 26.
We also know that Will made a total of 11 shots, so we can write another equation representing the total number of shots:
x + y = 11.
Now we have a system of two equations:
3x + 2y = 26,
x + y = 11.
To solve this system of equations, we can use the substitution method. We can isolate one variable in one equation and substitute its value into the other equation.
Let's solve the second equation for 'x':
x = 11 - y.
Now substitute this value of 'x' into the first equation:
3(11 - y) + 2y = 26.
Simplify the equation:
33 - 3y + 2y = 26.
Combine like terms:
-y = 26 - 33.
Simplify further:
-y = -7.
Multiply both sides by -1 to isolate 'y':
y = 7.
Now substitute this value of 'y' back into the equation x = 11 - y:
x = 11 - 7.
Simplify:
x = 4.
Therefore, Will made 4 three-point shots and 7 two-point shots.