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Lesson 2: Solutions to linear equations

# 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.

## Want to join the conversation?

• 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).
• Is there any other way to find the answer? How if we don't have the answers?
• Great question!

usually you will be able to find the solution, but there are times when the equation gets to complicated. there are formulas to help you solve certain types of equations that would be helpful.
(1 vote)
• So my math book says that I should rewrite the equation first, simplify it, then graph it. how do I rewrite it? I keep trying and I keep getting the wrong answer.
P.s. It gives me stuff like, 4X + Y = 6