Question

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?

Answer 1

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,, =)

Answer 2

4\x+@=3

Answer 3

4\x+2=3