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3 years ago

14

Using cramer’s rule, what is the value of y in the system of linear equations below? 2x-y=3 5x-2y=8

2 answers:

postnew [5]3 years ago

3 0

The answer is y=2×-3 and y=4-5/2x

scZoUnD [109]3 years ago

3 0

Answer:

The value of y is 1

Step-by-step explanation:

Given the system of linear equations

2x-y=3

5x-2y=8

we have to find the value of y using cramer’s rule

Cramer’s Rule is a method that uses determinants to solve the systems of equations that have same number of equations as that of variables.

The coefficient matrix is

$D=\begin{bmatrix}2&-1\\5&-2\end{bmatrix}$

$|D|=\begin{vmatrix}2&-1\\5&-2\end{vmatrix}=-4(-5)=-4+5=1$

For Y-matrix

$D_y=\begin{bmatrix}2&3\\5&8\end{bmatrix}$

$|D_y|=\begin{vmatrix}2 & 3\\5 & 8\end{vmatrix}=16-15=1$

By cramer's rule

$y=\frac{|D_y|}{|D|}=\frac{1}{1}=1$

Hence, value of y is 1

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(3a) You spend $72 on tapes and CDs. Each tape costs $8 and each CD costs $12.

Makovka662 [10]

Answer:

3a. 8t + 12c = 72

3b. t + c = 7

Step-by-step explanation:

number of tapes is t

number of Cds is c

so 8t + 12c = 72

and t + c = 7

so t = 7 - c

replace t = 7 - c in to the first equation

8(7 - c) + 12c = 72

56 - 8c + 12c = 72

4c = 72 - 56 = 16

c = 4

if c = 4, then t = 7 - c = 7 - 4 = 3

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1 year ago

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Archy [21]

Answer:

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Step-by-step explanation:

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2 years ago

jeyben [28]

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2 years ago

How can you solve:<br> = 30<br> Using the following numbers<br> 1, 3, 5, 7, 9, 11, 13, 15

suter [353]

The numbers you use are
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3 0

3 years ago

A sphere of radius 2x m has an area of 152.4 m2 and a volume of 360.9 m3. How much will the area and volume of another sphere

VladimirAG [237]

Answer:

$V = 1218.0375m^{3}$

$A = 342.9m^{2}$

Step-by-step explanation:

Area:

$A =$ π $r^{2}$

$152.4 =$ π $(2x)^{2}$ *Square 2x*

$152.4 =$ π $4x^{2}$ *Divide by π*

$48.510 = 4x^{2}$ *Divide by 4*

$12.128 = x^{2}$ *Square root*

$\sqrt{12.128} = x$ *Solve*

x ≈ 3.482

Now take the same equation but replace 2x with 3x

$A =$ π $r^{2}\\$

Now replace x with 3.482 and solve for area.

$A = 342.9m^{2\\}$

Volume:

$V = \frac{4}{3}$ π $r^{3}$ *Insert variables*

$360.9 = \frac{4}{3}$ π $(2x)^{3}$ *Cube 2x*

$360.9 = \frac{4}{3}$ π $(8x^{3})$ *Multiply $\frac{3}{4}$ on both sides*

$270.675 =$ π $(8x^{3})$ *Divide by π*

$86.159 = 8x^{3}$ *Divide by 8*

$10.770 = x^{3}$ *Cube root*

$\sqrt[3]{10.770} = x$ *Solve*

x ≈ 2.208

Now take the same equation but replace 2x with 3x

$V = \frac{4}{3}$ π $(3x)^{3}$

Now replace x with 2.208 and solve for volume.

$V = 1218.0375m^{3}$

4 0

2 years ago