All categories

3 years ago

Solve the system of equations - 8x - 5y = -13 and - 4x – 5y = 11 by combining the equations.

Mathematics

2 answers:

Natalija [7]3 years ago

5 0

Answer:

Your solution is (6, -7).

Step-by-step explanation:

Combining the equations is also known as substitution. This is done when you substitute one variable into another equation.

-8x - 5y = -13

-4x - 5y = 11

Let's change the second equation into one with one variable on each side.

-5y = 4x + 11

y = -4/5x - 11/5

Now, plug this into your first equation.

-8x - 5(-4/5x - 11/5) = -13

Distribute the -5 sign.

-8x + 4x + 11 = -13

Combine the like terms.

-4x + 11 = -13

-4x = -24

Isolate x by dividing both sides by -4.

x = -24/-4

x = 6

Now plug this back into either equation.

y = -4/5(6) - 11/5

Multiply.

y = -24/5 - 11/5

Subtract.

y = -35/5

Simplify.

y = -7

Your solution is (6, -7).

Check this by plugging in these values into the equation you have not checked yet.

-8(6) - 5(-7) = -13

-48 + 35 = -13

-13 = -13

Your solution is correct.

Hope this helps!

Citrus2011 [14]3 years ago

4 0

Answer:

(6,-7)

Step-by-step explanation:

subtract them:

-8x - 5y = -13

-4x - 5y = 11

you get

-4x = -24

so x = 6

plug x into the second equation:

-24 - 5y = 11

-5y = 35

y = -7

so your solution is (6,-7).

You might be interested in

Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velo

mr Goodwill [35]

Answer:

1350

Step-by-step explanation:

460 X 3

7 0

3 years ago

Fit a quadratic function to these three points: (-2,8), (0, -4), and (4, 68) Respuesta

zloy xaker [14]

Answer:

f(x) = 4x^2 + 2x - 4.

Step-by-step explanation:

Let the quadratic function be y = f(x) = ax^2 + bx + c.

For the point (-2, 8) ( x = -2 when y = 8) we have:

a(-2)^2 + (-2)b + c = 8

4a - 2b + c = 8 For (0, -4) we have:

0 + 0 + c = -4 so c = -4. For (4, 68) we have:

16a + 4b + c = 68

So we have 2 systems of equations in a and b ( plugging in c = -4):

4a - 2b - 4 = 8

16a + 4b - 4 = 68

4a - 2b = 12

16a + 4b = 72 Multiplying 4a - 2b = 12 by 2 we get:

8a - 4b = 24

Adding the last 2 equations:

24a = 96

a = 4

Now plugging a = 4 and c = -4 in the first equation:

4(4) - 2b - 4 = 8

-2b = 8 - 16 + 4 = -4

b = 2.

3 0

3 years ago

Priya's family exchanged 250 dollars for 4,250 pesos. Priya bout a sweater fo 510 pesos. How many dollars did the sweater cost?

Elena L [17]

30 dollars.

1 dollar = 17 pesos.

510 ÷ 17 =30

4 0

2 years ago

Read 2 more answers

What do you think is true of a line and a point not on the line? Explain

statuscvo [17]

The point is not a solution to the equation of the line.

Hope this helps!

3 0

3 years ago

Help with both questions offering 10 points

Alexandra [31]

Answer:

$\:\mathrm{First\: problem:\:}-2,\\\:\mathrm{Second\: problem:\: }-3$

Step-by-step explanation:

The slope of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

Plugging in any two points in the table we have:

First problem:

$m=\frac{1-5}{2-0}=\frac{-4}{2}=\fbox{$-2$}$

Second problem:

$m=\frac{-1-5}{2-0}=\frac{-6}{2}=\fbox{$-3$}$

8 0

3 years ago

Read 2 more answers