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4 years ago

15

Solve for x and y Y=6x-24 Y=9x

1 answer:

lorasvet [3.4K]4 years ago

6 0

Solve the following system:
{y = 6 x - 24
{x = 9 x

In the second equation, look to solve for x:
{y = 6 x - 24
{x = 9 x

Subtract 9 x from both sides:
{y = 6 x - 24
{-8 x = 0

Divide both sides by -8:
{y = 6 x - 24
{x = 0

Substitute x = 0 into the first equation:
{y = -24
{x = 0

Collect results in alphabetical order:
Answer: {x = 0
{y = -24

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Option C

When $(2x - 3)^2$ is subtracted from $5x^2$ then the result is $x^2 + 12x - 9$

<h3><u>Solution:</u></h3>

Given that $(2x - 3)^2$ is subtracted from $5x^2$

We have to find the result

Subtraction is a mathematical operation that tells us the difference between two numbers.

When "a" is subtracted from "b", we write in mathematical expression as "b - a"

So $(2x - 3)^2$ is subtracted from $5x^2$ is written mathematically as:

$\rightarrow 5x^2 - (2x - 3)^2$

<em><u>Expanding the above expression using algebraic identity:</u></em>

$(a-b)^2 = a^2 - 2ab + b^2$

$\rightarrow 5x^2 - ((2x)^2 -2(2x)(3) + (3)^2)\\\\\rightarrow 5x^2 - (4x^2 - 12x + 9)$

Multiplying the nnegative sign with terms inside bracket

<em><u>There are two simple rules to remember: </u></em>

When you multiply a negative number by a positive number then the product is always negative.

When you multiply two negative numbers or two positive numbers then the product is always positive.

$\rightarrow 5x^2 - (4x^2 - 12x + 9)\\\\\rightarrow 5x^2 - 4x^2 + 12x -9\\\\\rightarrow x^2 + 12x - 9$

Hence the result is: $x^2 + 12x - 9$

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