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 = ?.