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3 years ago

6

What is the answer for y=2x-5 and 4x-y=7

1 answer:

Dvinal [7]3 years ago

4 0

Substitute the first equation into the second equation. You will get:

4x - (2x - 5) = 7

Distribute the negative sign into the parenthesis:

4x - 2x + 5 = 7

Simplify

2x + 5 = 7

Subtract 5 on both sides

2x = 2

x = 1

Now, substitute x = 1 into the first equation:

y = 2(1) - 5

y = 2 - 5

y = -3

The solution to the system of equations is (1, -3).

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Answer: TRUE

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3 years ago

Solve: 5 - 3x < 20<br> Help

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Step-by-step explanation:

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3 years ago

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Select the statement that is true about squares from the choices below.

Leya [2.2K]

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4 years ago

For which pair of functions is the vertex of k(x)7 units below the vertex of f(x)?

kvv77 [185]

Answer: Option C

$f(x) = x^2;\ k (x) = x ^ 2 -7$

Step-by-step explanation:

Whenever we have a main function f(x) and we want to transform the graph of f(x) by moving it vertically then we apply the transformation:

$k (x) = f (x) + b$

If $b> 0$ then the graph of k(x) will be the graph of f(x) displaced vertically b units down.

If $b> 0$ then the graph of k(x) will be the graph of f(x) displaced vertically b units upwards.

In this case we have

$f (x) = x ^ 2$

We know that this function has its vertex in point (0,0).

Then, to move its vertex 7 units down we apply the transformation:

$k (x) = f (x) - 7\\\\k (x) = x ^ 2 -7$ .

Then the function k(x) that will have its vertex 7 units below f(x) is

$k (x) = x ^ 2 -7$

3 0

3 years ago

The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a

liubo4ka [24]

Answer:

$(x,y,z)=(1477, 1464, 1437)$

Step-by-step explanation:

Consider the selling of the units positive earning and the purchasing of the units negative earning.

<h3>Case-1:</h3>

Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
Mr.A earns Rs6000

So, the equation would be

$3x + 5y - 4z = 6000$

<h3>Case-2:</h3>

Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
Mr B neither lose nor gain meaning he has made 0₹

hence,

$2x - 3y + z = 0$

<h3>Case-3:</h3>

Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
Mr.C earns 13000₹

therefore,

$- x + 4y + 6z = 13000$

Thus our system of equations is

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>

we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\end{cases}\\\begin{cases}2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

Now solve the equation accordingly:

$\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}$

Solving the equation for x and y yields:

$\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}$

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

$\implies z= \dfrac{217000}{151}$

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437

6 0

3 years ago