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# Testing a solution to a system of equations

CCSS.Math:

## Video transcript

is negative one comma seven a solution for the system of linear equations below and they give us the first equation is X plus 2y is equal to 13 second equation is 3x minus y is equal to negative 11 in order for negative 1 comma 7 to be a solution for the system it needs to satisfy both equations or another way of thinking about it x equals 7 and y I'm sorry X is equal to negative 1 this is the x coordinate x equals negative 1 and y is equal to 7 need to satisfy both of these equations in order for it to be a solution so let's try it out let's try it out with the first equation so we have X plus 2y is equal to 13 so if we're thinking about that we're testing to see if when X is equal to negative 1 and Y is equal to 7 well X plus 2y equal 13 so we have negative 1 plus 2 times 7 y should be 7 this needs to be equal to 13 and I'll put a question mark there because we don't know whether it does so this is the same thing as negative 1 plus 2 times 7 plus 14 that does indeed equal 13 this is negative 1 plus 14 this is 13 so 13 does it does definitely equal 13 so it this this point it does at least satisfy this first equation this point does sit on the graph of this first equation or on the line of this first equation now let's look at the second equation I'll do that one in blue we have 3 times negative 1 3 times negative 1 minus y so minus 7 needs to be equal to negative 11 and I'll put a question mark here because we don't know whether it's true or not so let's see we have 3 times negative 1 is negative 3 and then we have minus 7 needs to be equal to negative 11 put the question mark there negative 3 minus 7 that's negative 10 so we get negative 10 equaling negative 11 no negative 10 does not equal a negative 11 so the neg X equaling negative 1 and Y equaling seven does not satisfy the second equation so it does not sit on its graph so this over here is not is not a solution for the system so the answer is no it satisfies the first equation but it doesn't satisfy the second in order to be a solution for the system it has to satisfy both equations