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Worked example: solutions to 2-variable equations

How do you check if an ordered pair is a solution to a given equation? You need to plug in the numbers and see what equality results. Watch this video to see a worked example.

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• At , would the equation y = -2+ 4/3y be equivalent?
• what if you are not given an ordered pair and you have to figure out this equation
• How are you going to create an equation if you are not given at least one ordered pair? The ordered pair could be implied by giving the x or y intercept, but it is still an ordered pair.
• Is there an easy way to narrow down the answer besides go through each answer one by one? If so what is it?
• No, even if simplified there would be an infinite amount of values for x and y that satisfy the question. This the question is asking which would be a plausible solution so plugging in is the only option in this scenario.
• I must be missing something that was already said, or something I don't know. But if the equation is like y = -2x - 5. Could you still be able to do what he is doing in the video? I feel like you can but how?
• You can! Anytime you are asked to determine if a point (an ordered pair of (x,y)) is a solution, we use substitution. We use the x-value for "x" in the equation and the y-value for "y" in the equation.

Example: Is (2, 3) a solution to your equation: y = -2x - 5?
Substitute: `3 = -2(2) - 5`
Simplify the right side:
`3 = -4 - 5`
`3 = -9`
Since these are not equal, we know the point (2,3) is not a solution to this equation. Or, is not a point on the line that is created from this equation.

If the 2 sides turn out to be equal, then you know the point is a solution to the equation.
Hope this helps.
• What is an "ordered" pair?
• A point on the coordinate plane that gives the horizontal distance from the origin (x) and the vertical distance (y) that is in the form (x,y). If you create a table from a linear equation, you get a series of ordered pairs.
• how do you figure the value of x and y
(1 vote)
• You can pick any number to use for one of the variables. Plug it into the equation to calculate the other variable. For example: 2x+3y=12
If x=2: 2(2)+3y = 12
-- Simplify: 4+3y = 12
-- Subtract 4 from both sides: 3y = 8
-- Divide both sides by 3: y = 8/3 or 2 2/3
-- You now have a point on the line: (2, 2 2/3)

In the video, Sal is given points to test. In that situation, you replace each variable with their given value and see if the 2 sides are equal. Remember, ordered pairs are always (x,y). So, the first value is X and the 2nd value is Y.

Hope this helps.
• does this cover absolute vale equalities and inequalities
(1 vote)
• I saw nothing here about absolute values which would look like "|x|" or |3|=3 or |-3|=3 OR |-9|=9
The best way to think about absolute values is- "No matter the sign (+ or -) the number remains positive, because the absolute value cannot be negative" Hope that helps. Now inequalities, something simple like....... 1<x<3 where "x" is greater then 1 but less then 3.. The interval notation would be (SET BUILDER NOTATION!)----> {x|x>1, x<3} or (INTERVAL NOTATION(WHICH IS INCLUDING A UNION aka "U"))--> (1,x)U(x,3)...... if the sign was a "greater than or equal to, or less than or equal to" then the interval notation would be [1,x]U[x,3].... I hope this helps.
• between x and y what is the slope and the intercept?
• Most lines have 2 intercepts: an x-intercept and a y-intercept. The x-intercept occurs where y=0 which places the point on the x-axis. The y-intercept occurs where x=0 which places the points on the y-axis.

Lines that have only one intercept are: a) Lines that cross both the x & y axis at the origin (0,0), and b) vertical and horizontal lines which only cross one axis.

To find the slope of a line, you need two points that are on the line, then you would use the slope formula: m = (y2-y1)/(x2-x1). Or, if your equation is in slope intercept form (y = mx + b), then you can read the slope from the line. The number (m) that is the coefficient of "x" is the slope. And, the constant term (b) is the y-intercept at (0,b).