Answer:
[tex]2x+3y=21\\x=2y[/tex]
x represents the number of two-point shots. y represent the number of three-point shots.
Step-by-step explanation:
Let's let x represent the number of two-point shots Easton made and let's let y represent the number of three-point shots Easton made.
So, we know that that Easton scored a total of 21 points.
In other words, the amount of two-point shots and amount of three-point shots total 21. In an equation, this is:
[tex]2x+3y=21[/tex]
The 2 in front of the x represents the two-point per shot, and the 3 in front of the y represents the three-point per shot.
We also know that Easton made twice as many two-point shots as three-point shots. So, we can write this as:
[tex]x=2y[/tex]
The number of two-pointers x is equivalent to twice the number of three-pointers y.
So, our system of equations is as follows:
[tex]2x+3y=21\\x=2y[/tex]
Notes:
To solve, use substitution. Substitute the second equation into the first:
[tex]2(2y)+3y=21[/tex]
Multiply:
[tex]4y+3y=21[/tex]
Combine like terms:
[tex]7y=21[/tex]
Divide by 7:
[tex]y=3[/tex]
Solve for x using the second equation again:
[tex]x=2(3)=6[/tex]
So, Easton made 6 two-pointers and 3 three-pointers.
