Question

during their last game, the miami dolphins scored 6 times for a total score of 30 points. They scored 7 points for each touchdown and 3 points for each field goal. Write and solve the system of equations to find the total of touchdowns and field goals scored.

Answer 1

Miami dolphins scored 3 touchdowns and 3 field goals.

Explanation:

Let x be the number of touchdowns and y be the number of field goals.

It is given that during their last game, the miami dolphins scored 6 times for a total score of 30 points.

`x+y=6` .... (1)

They scored 7 points for each touchdown and 3 points for each field goal.

`7x+3y=30` .... (2)

Use substitution method to solve the system of equations.

Substitute value of y( in terms of x) in equation (2) from equation (1).

`7x+3(6-x)=30`

`7x+18-3x=30`

Combine like terms.

`4x+18=30`

Subtract 18 from both sides.

`4x+18-18=30-18`

`4x=12`

Divide both sides by 4.

`x=(12)/(4)`

`x=3`

The value of x is 3.

Substitute x=3 in equation (1), to find the value of y.

`3+y=6`

Subtract 3 from both sides.

`y=6-3`

`y=3`

The value of y is 3.

Therefore Miami dolphins scored 3 touchdowns and 3 field goals.

Answer 2

Answer: The total of touchdowns and field goals scored are 3 and 3 respectively.

Explanation:

Since we have given that

The miami dolphins scored 6 times for a total score of 30 points .

Let the total of touch downs scored be x

Let the total of field goals scored be y

Number of points for each touchdown = 7

Number of points for each field goal = 3

According to question,

`x+y=6\\\\7x+3y=30`

Now, we will use

`\mathrm{Subsititute\:}x=6-y\\\\\begin{bmatrix}7\left(6-y\right)+3y=30\end{bmatrix}`

`\begin{bmatrix}7\left(6-y\right)+3y=30\end{bmatrix}\\\\42-7y+3y=30\\\\42-4y=30\\\\-4y=30-42\\\\-4y=-12\\\\y=(12)/(4)\\\\y=3`

Now, Substitute the value of y in

`x=6-y\\\\x=6-3\\\\x=3`

Hence, The total of touchdowns and field goals scored are 3 and 3 respectively.