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#