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3 years ago

Solve the System of Equations

Mathematics

1 answer:

Softa [21]3 years ago

3 0

<u>Answer: </u>

The ordered pair value of (x, y) is (6,-11)

<u>Solution: </u>

Given Equations are

Let 8x + 15y = -117 be Equation 1 and 4x + 9y=-75 be Equation 2.

Solving Equations 1 and 2 to get the value of x and y.

Multiply Equation 2 with 4.

16x + 36y = -300

On dividing the above expression by 2, we get

8x + 18y = -150 (Change the sign to get the value of y).

-8x - 18y = 150 --- eqn 3

Now solving eqn 1 and eqn 3

8x + 15y = -117

-8x - 18y = 150

By cancelling 8x and -8x in eqn 1 and eqn 3

-3y = 33

y = -11

Substitute the value y in Equation 2.

4x + 9 (-11) = -75

4x – 99 = - 75

4x= -75 +99

4x = 24

x=6

Hence the value of x and y is (6,-11).

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2 years ago

After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets

Alinara [238K]

Answer:

Option a : $y-300 = 4(x - 100)$

Step-by-step explanation:

Given :

The drama club sold 100 tickets to a show, it had $300 in profit.

The next show, it had sold a total of 200 tickets and had a total of $700 profit.

To Find : Equation models the total profit, y, based on the number of tickets sold, x

Solution :

For 100 tickets he had $300 in profit .

⇒ ( $x_{1} ,y_{1}$ )=(100,300)

For 200 tickets he had $700 in profit .

⇒ ( $x_{2} ,y_{2}$ )=(200,700)

We will use point slope form i.e.

$y-y_{1} = m(x - x_{1})$ --(A)

Now, to calculate m we will use slope formula :

$m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

$m = \frac{700 -300}{200-100}$

$m =4$

Now, putting values in (A)

$y-300 = 4(x - 100)$

Thus Option a is correct i.e. $y-300 = 4(x - 100)$

5 0

3 years ago

Read 2 more answers

For which positive integer values of $k$ does $kx^2+20x+k=0$ have rational solutions? Express your answers separated by commas a

Musya8 [376]

Answer:

-10,10

Step-by-step explanation:

The given quadratic equation is

$k {x}^{2} + 20x + k = 0$

The discriminant of this equation is given by;

$D = {b}^{2} - 4ac$

where a=k, b=20, c=k

For rational solutions, the discriminant must be zero.

${20}^{2} - 4 \times k \times k = 0$

Simplify to get:

$400 - 4 {k}^{2} = 0$

This implies that:

$400 = 4 {k}^{2}$

$100 = {k}^{2}$

Take square root to get:

$k = \pm\sqrt{100}$

$k = \pm10$

$k = - 10 \: or \: k = 10$

3 0

3 years ago