Question

On a math test, Stephen missed 3 computation problems and 1 word problem for a total of 9 points off. Brad missed 2 computation problems and 2 word problems for a total of 10points off. This relationship can be represented by the system of equations below, where x stands for the point value of computation problems missed and y stands for the point valueof word problems missed.3x + y = 92x+2y= 10

Answer 1

The system of equations is

`\begin{cases}3x+y=9 \\ 2x+2y=10\end{cases}`

To solve that system let's subtract the equation, but first, one of the variables must have the same coefficient, to do that, let's divide the second equation by 2

`\begin{cases}3x+y=9 \\ 2x+2y=10\text{ (}/\text{2)}\end{cases}\Rightarrow\begin{cases}3x+y=9 \\ x+y=5\end{cases}`

Now we have

`\begin{cases}3x+y=9 \\ x+y=5\end{cases}`

If we subtract the equations

`\begin{gathered} (3x+y)-(x+y)=9-5 \\ \\ 2x=4 \\ \\ x=2 \end{gathered}`

Then x = 2, it means that the point value of computation problems missed is equal to 2. Now we have the value of x we can use any equation to solve it for y.

`\begin{gathered} x+y=5 \\ \\ 2+y=5 \\ \\ y=3 \end{gathered}`

Therefore y = 3, the point value for each word problem is 3 points