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3 years ago

Solve the system of equations below: 5x-2y=18 3x+3y=15

Mathematics

2 answers:

jarptica [38.1K]3 years ago

5 0

Answer : The value of x and y is, 4 and 1 respectively.

Step-by-step explanation :

The given equations are:

$5x-2y=18$ ..........(1)

$3x+3y=15$ ..........(2)

Using substitution method,

$5x-2y=18$

$5x=18+2y$

$x=\frac{18+2y}{5}$ ...........(3)

Now putting equation 3 in 2, we get the value of y.

$3x+3y=15$

$3(\frac{18+2y}{5})+3y=15$

$(\frac{54+6y}{5})+3y=15$

$54+6y+15y=75$

$6y+15y=75-54$

$21y=21$

$y=1$

Now putting value of y in equation 3, we get the value of x.

$x=\frac{18+2y}{5}$

$x=\frac{18+2\times 1}{5}$

$x=\frac{18+2}{5}$

$x=4$

Thus, the value of x and y is, 4 and 1 respectively.

Lady_Fox [76]3 years ago

4 0

X = 4

y = 1

I hope this helps. :)

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Answer:

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Step-by-step explanation:

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3 years ago

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Vanyuwa [196]

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3 years ago

Which relationship is a direct variation?

Setler79 [48]

Option A is the relationship which shows a direct variation.

Step-by-step explanation:

The direct variation is a relationship between two variables in which one is the multiple of the other. It is given by the relation

$\frac{y}{x}=k$

Option A:

For $x=2$ and $y=1$ ,

$\frac{y}{x}=\frac{1}{2}$

For $x=4$ and $y=2$ ,

$\frac{y}{x}=\frac{2}{4}= \frac{1}{2}$

Since, the constant k is equal for all the values of x and y in the table, this relationship is a direct variation.

Option B:

For $x=2$ and $y=4$ ,

$\frac{y}{x}=\frac{4}{2}= 2$

For $x=4$ and $y=16$ ,

$\frac{y}{x}=\frac{16}{4} =4$

Since, the values of constant k is not equal for all the values of x and y in the table, this relationship is not a direct variation.

Option C:

For $x=1$ and $y=3$

$\frac{y}{x} =\frac{3}{1} =3$

For $x=2$ and $y=5$

$\frac{y}{x} =\frac{5}{2}$

Since, the values of constant k is not equal for all the values of x and y in the table, this relationship is not a direct variation.

Option D:

For $x=1$ and $y=-1$

$\frac{y}{x} =\frac{-1}{1} =-1$

For $x=2$ and $y=2$

$\frac{y}{x} =\frac{2}{2} =1$

Since, the values of constant k is not equal for all the values of x and y in the table, this relationship is not a direct variation.

Thus, Option A is the relationship which shows direct variation.

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4 years ago

1. A right triangle has a hypotenuse of length 10 yd and one leg of length 2 yd.

Aleonysh [2.5K]

Question 1.

The Pythagoras Theorem states that the square of the hypotenuse is equal to the sum of the square of the two legs.

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This implies that,

$10^2=l_1^2+ {2}^{2}$

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The correct answer is C

Question 2

We want to solve

${e}^{4x} = 11$

using inverse functions.

The inverse of an exponential function is a logarithmic function.

We take natural log of both sides to get;

$ln({e}^{4x}) = \ln(11)$

Recall that

$\ln( {a}^{n} ) = n \ln(a)$

This means

$4x \ln({e}) = \ln(11)$

Logarithm of the base is 1

$4x (1) = \ln(11)$

$4x = \ln(11)$

Divide both sides by 4

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3 years ago

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3 years ago