solve 3x-6y=18 for y; show (2,4) soln for 3x+4y=22; slopes &

[AprilHite]

1) Given the following equation, 3x – 6y = 18; solve for y.

2) Verify that the ordered pair (2, 4) is a solution to the equation 3x + 4y = 22

3) For the following equation: 3x – 2y = 11:
Find x if y = 2
Find y if x = 1/3
Present the solutions as ordered pairs.

4) Find the slope and the y-intercept of the line represented by the equation: -3x + 4y = 8

5) Write the equation of a line in slope-intercept form with the slope of -2/5 and y-intercept (0, -3).

I am having problems with these

[DAiv]

This site has lots of useful information on how to solve such problems in the Beginning Algebra Topics section.

In particular,

Solving Linear Equations
Slope of a Straight Line
Slope and y-intercept
Intercepts

Have a read through those and hopefully things will be a little clearer.

DAiv

[AprilHite]

Hi, Those sites helped but I am still lost on a few of these questions and also can someone check and make sure the oens I did are right and maybe help me with the ones I could not answer. Please and thanks

1. 3x-6y=18
Since 3x does not contain a variable to solve for, move it to the right hand side of the equation by subtracting 3x from both sides

-6y=-3x+18

Divide each term in the equation by -6

-6y/ -6 = -3x/ -6 + 18/ -6

Simplify the left hand side by canceling the common factors

Y= -3x / -6 + 18/ -6

Simplify the right hand side by simplifying each term

Y= x/2-3

2. 3x+4y=22 is (2,4) the solution

3. in the following equation find x if y is 2

3x-2y=11

3x-2(2) =11

multiply -2 by each term inside the parenthesis

3x-4=11

Since -4 does not contain the variable to solve, move it to the right hand side by adding 4 to both side

3x=4+11 add 11 to 4 to get 15

3x=15

Divide each term by 3

3x/ 3 = 15/ 3

Simplify the left hand side by canceling common factor

x= 15/3

simplify the right hand side by simplifying each term

x=5

Now for the following equation 3x-2y=11 find y if x = 1/3

3x-2(1/3) =11

Multiply -2 by each term indie the parenthesis

3x- 2/3=11 since -2/3 does not contain the variable to solve move it to the right hand side by adding 2/3 to both sides.

3x=2/3+11

simplify the right hand of the equation

3x= 35/3
divide each term by 3

3x/3 = 35/3 * 1/3

Simplify the left side by cancelling the common factors

x= 35/3 * 1/3

x= 35/9

4. Find the slope of the y-intercept of -3x+4y=8

Since -3x does not contain the variable to solve move to right hand side by adding 3x to both sides

4y=3x+8
Divide each term by 4
4y/4 = 3x/4 + 8/4

simplify by canceling common factors

y= 3x/4 + 8/4

simplify the right hand side by simplifying each term

y= 3x/4+2

To find the slope and the y intercept use the y=mx+b formula m=slope and B is y intercept

y=mx+b

m=3/4 and b=2

m= ¾, b=2

5. Write the equation of the line in slope intercept form with the slope
-2/5 and y intercept (0. -3)

[DAiv]

Q1.

Given the following equation, 3x – 6y = 18; solve for y.

Looks good and the working is well laid out and easy to follow.

Be careful, though, when writing variables to make sure that if you start with a lower case variable, it remains lower case throughout. For example, y does not become Y, since technically, they are different variables.


Q2.

Verify that the ordered pair (2, 4) is a solution to the equation 3x + 4y = 22

(2,4) is an ordered pair, meaning that there are two numbers, and that the order those numbers are written in is important. That is, (2,4) and (4,2) mean different things. Here, (2,4) is a cartesian coordinate, where the first number in parentheses (round brackets) represents the x-coordinate (how far to the right the point is on a graph), and the second number represents the y-coordinate (how far up the point is on a graph).

So, when the question says, "Verify that the ordered pair (2, 4) is a solution to the equation 3x + 4y = 22", it's telling you that the x-coordinate is 2 (x=2), and the y-coordinate is 4 (y=4). Now, you just have to plug those values into the equation and check that 3x + 4y really does equal 22.


Q3.

For the following equation: 3x – 2y = 11:
Find x if y = 2
Find y if x = 1/3
Present the solutions as ordered pairs.

[Find x if y = 2.]
The working looks good. The solution needs to be written as an ordered pair, which hopefully the explanation in the previous question will now allow you to do.

[Find y if x = 1/3.]
It looks as if you misread the question. You have solved for x given that y = 1/3, rather than solving for y given that x = 1/3. (Plus, the new solution will also need to be written as an ordered pair.)


Q4.

Find the slope and the y-intercept of the line represented by the equation: -3x + 4y = 8

Looks good. It's usually good practice to state your answer in words at the end, underlined, so that anyone reading it can skip straight to it and know exactly what the answer is, without having to backtrack and find out what m and b stand for.

e.g. The slope is 3/4 and the y-intercept is 2.


Q5.

Write the equation of the line in slope intercept form with the slope
-2/5 and y intercept (0. -3)

Hopefully, having read earlier about what the ordered pair (0, -3) means, using your knowledge of the equation of a straight line, y = mx + b, and how each part affects how the line appears on a graph, you'll now be able to extract the relevant numbers from the question and plug them into the equation, giving y = ?.


DAiv