How to construct simulataneous equation through extended responses?

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Can someone please explain to me how to do question 4? Thanks!

1 Answer
Dec 5, 2017

John scored 4 field goals.
David scored 8 field goals.

Explanation:

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Let's say u is number of field goals and w is number of free throws. Then we can say:

John's points come from u field goals and w free throws. Since field goal is 2 points and free throw is 1 point, we can write the equation for his score as follows:

u(2)+w(1)=11

David had twice the number of field goals, i.e. 2u, and same number of free throws, i.e. w. We can write the second equation from David's performance:

2u(2)+w(1)=19

Simplifying, we get the following system of equations we can use to solve for u and w:

2u+w=11
4u+w=19

We will multiply the top equation by -1:

-2u-w=-11
4u+w=19

Adding the two equations together, the w and -w cancel and we get:

2u=8

u=4

Now we plug this into John's equation to solve for w:

2(4)+w=11
8+w=11
w=11-8=3