Question

I just need a little help , I don’t understand

Answer 1

Let x represent the number of touchdowns,

let y represent the number of field goals.

Given that the number of field goals was 1 more than twice the number of touchdown, this implies that

`\begin{gathered} y=1+2x \\ \Rightarrow x-2y=1 \end{gathered}`

7 points is earned for touchdown, and 3 points for each field goal. If a total of 55 points is earned, this implies that

`7x+3y=55`

Thus, the system of equations that best represent this situation is

`\begin{gathered} 2x-y=-1 \\ 7x+3y=55 \end{gathered}`

To solve the number of touchdowns and number of field goals, we solve the simultaneous equations:

`\begin{gathered} 2x-y=-1\text{ ----- equation 1} \\ 7x+3y=55\text{ ---- equation 2} \end{gathered}`

Using the method of substitution,

step 1: From equation 1, make y the subject of the formula.

`\begin{gathered} 2x-y=-1 \\ \Rightarrow y=1+2x\text{ ----equation 3} \end{gathered}`

step 2: Substitute equation 3 into equation 2.

`\begin{gathered} 7x+3y=55 \\ 7x+3(1+2x)=55 \\ \\ \end{gathered}`

step 3: Open parentheses and collect like terms.

`\begin{gathered} 7x+3+6x=55 \\ 13x=52 \\ \end{gathered}`

step 4: Divide both sides of the equation by the coefficient of x.

The coefficient of x is 13.

Thus,

`\begin{gathered} (13x)/(13)=(52)/(17) \\ \Rightarrow x=4 \end{gathered}`

step 5: Substitute the obtained value of x into equation 3.

Thus,

`\begin{gathered} y=1+2x \\ =1+2(4) \\ \Rightarrow y=9 \end{gathered}`

Hence,

Number of touchdowns x:

`4`

Number of field goals y:

`9`