Worked example: solutions to 2-variable equations
About this video
Sal tests whether (3, 2) and (2, 3) are solutions of 4x - 1 = 3y + 5. Substituting (3, 2) gives 11 = 11, so it is a solution; (2, 3) gives 7 = 14, which is false, so only (3, 2) works.
You'll be able to
- substitute an ordered pair into an equation with variables on both sides.
- decide whether an ordered pair is a solution by checking if both sides are equal.
Key words
- ordered pair
- Two numbers (x, y); the first is x and the second is y.
- solution
- A pair of values that makes both sides of the equation equal.
- satisfy
- To make an equation true.
Transcript
- [Voiceover] "Which of the ordered pairs is a "solution of the following equation?" 4x minus one is equal to 3y plus five. Now, when we look at an ordered pair we wanna figure out whether it's a solution, we just have to remind ourselves that in these ordered pairs the convention, the standard, is is that the first coordinate is the x coordinate, and the second coordinate is the y coordinate.
So they're gonna, if this is a solution, if this ordered pair is a solution, that means that if x is equal to three and y is equal to two, that that would satisfy this equation up here. So let's try that out. So, we have four times x. Well we're saying x needs to be equal to three, minus one, is going to be equal to three times y.
Well, if this ordered pair is a solution then y is going to be equal to two, so three times y, y is two, plus five. Notice all I did is wherever I saw the x, I substituted it with three, wherever I saw the y, I substituted it with two. Now let's see if this is true.
Four times three is twelve, minus one. Is this really the same thing as three times two which is six, plus five? See, 12 minus one is 11, six plus five is also 11. This is true, 11 equals 11. This pair three, two does satisfy this equation. Now let's see whether this one does, two, three.
So this is saying when x is equal to two, y would be equal to three for this equation. Let's see if that's true. So four times x, we're now gonna see if when x is two, y can be three. So four times x, four times two, minus one is equal to three times y, now y we're testing to see if it can be three.
Three times three plus five, let's see if this is true. Four times two is eight, minus one, is this equal to three times three? So that's nine plus five. So is seven equal to 14? No, clearly seven is not equal to 14. So these things are not equal to each other.
So this is not a solution, when x equals two y cannot be to three and satisfy this equation. So only three, two is a solution.
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