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3 years ago

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13. Solve the following system by any method. 8x + 9y = –5 –8x – 9y = 5

2 answers:

Nady [450]3 years ago

7 0

Just add the like terms together.

Roman55 [17]3 years ago

6 0

Answer: <span><span>the system is indeterminate and has infinite solutions.

Justification.</span>

1) System:

Given:

8x + 9y = –5
–8x – 9y = 5

2) I will show you that system is not determined:

Add the two equations:

8x - 8x + 9y - 9y = - 5 + 5

0 = 0

3) You have gotten an identity which is true for all x, meaning that there are infinite solutions.

So, the answer is that the system is indeterminate and has infinite solutions.

Do you know why does that happen?

It is because the two equations are equivalent, meaning that they are the same line.

You can prove that the two equations are equivalent by multiplying any of them by -1, which will turn one equation into the other.

For example, multiply 8x + 9y = - 5 times - 1:

=> - 8x - 9y = 5,which is the second equation.
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Read 2 more answers

What is the result of a dilation of scale factor 3 centered at the origin of the line 2y + 3x=10?? PLEASE HELP PLEASEEEEEEEEE

maks197457 [2]

Given:

The equation of a line is:

$2y+3x=10$

The line is dilated by factor 3.

To find:

The result of dilation.

Solution:

The equation of a line is:

$2y+3x=10$

For $x=0$ ,

$2y+3(0)=10$

$2y+0=10$

$y=\dfrac{10}{2}$

$y=5$

For $x=2$ ,

$2y+3(2)=10$

$2y+6=10$

$2y=10-6$

$2y=4$

Divide both sides by 2.

$y=\dfrac{4}{2}$

$y=2$

The given line passes through the two points A(0,5) and B(2,2).

If the line dilated by factor 3 with origin as center of dilation, then

$(x,y)\to (3x,3y)$

Using this rule, we get

$A(0,5)\to A'(3(0),3(5))$

$A(0,5)\to A'(0,15)$

Similarly,

$B(2,2)\to B'(3(2),3(2))$

$B(2,2)\to B'(6,6)$

The dilated line passes through the points A'(0,15) and B'(6,6). So, the equation of dilated line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-15=\dfrac{6-15}{6-0}(x-0)$

$y-15=\dfrac{-9}{6}(x)$

$y-15=\dfrac{-3}{2}x$

Multiply both sides by 2.

$2(y-15)=-3x$

$2y-30=-3x$

$2y+3x=30$

Therefore, the equation of the line after the dilation is $2y+3x=30$ .

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3 years ago