Question

How to construct simulataneous equation through extended responses?

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

Answer 1

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`