An expression is shown below:

Mathematics

1 answer:

Alex73 [517]3 years ago

3 0

Given:

The given expression is:

$6x^2y-3xy-24xy^2+12y^2$

To find:

Part A: The expression by factoring out the greatest common factor.

Part B: Factor the entire expression completely.

Solution:

Part A:

We have,

$6x^2y-3xy-24xy^2+12y^2$

Taking out the highest common factor 3y, we get

$=3y(2x^2-x-8xy+4y)$

Therefore, the required expression is $3y(2x^2-x-8xy+4y)$ .

Part B:

From part A, we have,

$3y(2x^2-x-8xy+4y)$

By grouping method, we get

$=3y(x(2x-1)-4y(2x-1))$

$=3y(x-4y)(2x-1)$

Therefore, the required factored form of the given expression is $3y(x-4y)(2x-1)$ .

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3y-6=3x and y+2x=5 solve the system of linear equations by graphing PLEASE SHOW WORK

Dmitry_Shevchenko [17]

Answer:

(x, y) = (1, 3)

Step-by-step explanation:

The "work" of solving by graphing is typing the equations into a graphing calculator and highlighting the point of intersection.

___

If you're graphing these by hand, there are a couple of strategies you can use. One is to make use of the intercepts of the line. For each of these, you need to rearrange the equation to a suitable form.

3y -6 = 3x

To put this into "intercept form", put the variable terms on one side of the equal sign and the constant on the other. Then divide by the constant and express the resulting variable coefficients as denominators.

3x -3y = -6

x/(-6/3) +y/(-6/-3) = 1

x/(-2) + y/2 = 1 . . . . . . The x-intercept is -2; the y-intercept is 2.

Plot the intercept points and draw a line through them.

y +2x = 5

The intercepts for this one are found by dividing by 5:

x/(5/2) + y/5 = 1 . . . . . . The x-intercept is 2.5; the y-intercept is 5.

The other strategy you can use for this one is to rearrange the equation to slope-intercept form and make use of those numbers.

y = -2x + 5

The y-intercept is 5 (as we already found above), and the slope is -2. That means the line drops 2 units for each unit it goes to the right. Apart from the y-intercept, other points on this line will be (1, 3), (2, 1), (3, -1).

Solution

When you plot these lines, you find they intersect at (1, 3). That is the solution to the system of equations, the values of x and y that satisfy both equations.