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# Worked example: solutions to 2-variable equations

CCSS.Math:

## Video transcript

which of the ordered pairs is a solution of the following equation 4x minus 1 is equal to 3 y plus 5 now when we look at an ordered pair and we want to figure out what's 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 going to if this is a solution if this ordered pair is a solution that means that if X is equal to 3 and Y is equal to 2 that that would satisfy this equation up here so let's try that out so we have 4 times X well we're saying X needs to be equal to 3 minus 1 is going to be equal to 3 times y well if this ordered pair is a solution then Y is going to be equal to 2 so 3 times y Y is 2 plus 5 notice all I did is wherever I saw the X I substitute it with 3 wherever I saw the Y I substituted it with 2 now let's see if this is true 4 times 3 is 12 minus 1 is this really the same thing as 3 times 2 which is 6 plus 5 see 12 minus 1 is 11 6 plus 5 is also 11 this is true 11 equals 11 this this pair three comma two does satisfy this equation now let's see whether this one does 2 comma 3 so this is saying when X is equal to 2 y would be equal to 3 for this equation let's see if that's true so 4 times X we're now going to say see if if when X is 2 y can be 3 so 4 times X 4 times 2 minus 1 is equal to 3 times y now why we're testing to see if it can be 3 3 times 3 plus 5 let's see if this is true 4 times 2 is 8 minus 1 is this equal to 3 times is this equal to 3 times 3 so that's 9 plus 5 so is 7 equal to 14 no clearly 7 is not equal to 14 so these things are not equal these things are not equal to each other so this is not a lucien when x equals two y cannot be equal to equal to three and satisfy this equation so only three comma two is a solution