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3 years ago

What is the y-value in the solution to this system of linear equations?

Mathematics

2 answers:

coldgirl [10]3 years ago

8 0

Answer:

A. -4

Step-by-step explanation:

To find the y-value in the solution to this system of linear equation, we will follow the steps below:

4x + 5y = −12 ------------------------------------------------------(1)

-2x + 3y = −16 -----------------------------------------------------(2)

Multiply through equation (1) by 2 and multiply through equation (2) by 4 to make the x coefficient have equal value

8x + 10y = -24 ---------------------------------------------------(3)

-8x + 12y = -64 ---------------------------------------------------(4)

Add equation (1) and equation (2)

22y = -88

Divide both-side of the equation by 22

22y/ 22 = -88/ 22

y =-4

Westkost [7]3 years ago

3 0

Answer:

Step-by-step explanation:

Given the 2 equations

4x + 5y = - 12 → (1)

- 2x + 3y = - 16 → (2)

Eliminate the x- term by multiplying (2) by 2 and adding the result to (1)

- 4x + 6y = - 32 → (3)

Add (1) and (3) term by term

11y = - 44 ( divide both sides by 11 )

y = - 4

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skelet666 [1.2K]

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3 years ago

5/6=x-10/3x+6 solution?

Ivan

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{x = - 10}}}}}$

Step-by-step explanation:

$\sf{ \frac{5}{6} = \frac{x - 10}{3x + 6} }$

Apply cross product property

⇒ $\sf{5(3x + 6) = 6( x - 10)}$

Distribute 5 through the parentheses

⇒ $\sf{15x + 30 = 6( x - 10)}$

Distribute 6 through the parentheses

⇒ $\sf{15x + 30 = 6x - 60}$

Move 6x to left hand side and change it's sign

⇒ $\sf{15x - 6x + 30 = - 60}$

Collect like terms

⇒ $\sf{9x + 30 = - 60}$

Move 30 to right hand side and change it's sign

⇒ $\sf{9x = - 60 - 30}$

Calculate

⇒ $\sf{9x = - 90}$

Divide both sides of the equation by 9

⇒ $\sf{ \frac{9x}{9} = \frac{ - 90}{9} }$

Calculate

⇒ $\sf{x = - 10}$

Hope I helped!

Best regards!!

3 0

3 years ago

Write the equation of the line, in point-slope form. Identify the point (-2, -2) as (x1, y1). Use the box provided or the upload

zimovet [89]

Answer:

m = (2-(-2))/(2-(-2)) = 4/4 = 1
y +2 = 1(x +2)

Step-by-step explanation:

The point-slope form of the equation for a line with slope m through point (x1, y1) is ...

y -y1 = m(x -x1)

To find the slope of the line, find the ratio of the difference in y-values of the points to the difference in corresponding x-values. Here, the slope is ...

m = (2 -(-2))/(2 -(-2)) = 4/4 = 1 . . . work to compute slope

The problem statement tells you x1 = -2, y1 = -2. Putting the numbers in to the point-slope form gives ...

y -(-2) = 1(x -(-2))

y + 2 = x + 2 . . . equation form with m, (x1, y1) filled in

The answer at the top leaves the slope shown as 1. We don't know how much simplification you are expected to do. Obviously, this <em>could</em> be simplified to y=x, but then the use of (-2, -2) for the point would not be obvious.

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3 years ago

How to prove the pythagorean Theorem pictorially

Irina18 [472]

By drawing the hypotenuse of the shape.

5 0

3 years ago

Calculus piecewise function.

Kipish [7]

Part A

The notation $\lim_{x \to 2^{+}}f(x)$ means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows $\lim_{x \to 2^{+}}f(x) = 2$

Then for the left hand limit $\lim_{x \to 2^{-}}f(x)$ , we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, $\lim_{x \to 2^{-}}f(x) = 1$

===============================================================

Part B

Because $\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)$ this means that the limit $\lim_{x \to 2}f(x)$ does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since $\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3$ , this means the limit $\lim_{x \to 4}f(x)$ does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

4 0

1 year ago