Find all solutions of the given system of equations and...

Find all solutions of the given system of equations and check your answer graphically. HINT [First eliminate all fractions and decimals.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).) -3/4x + y/3 = -5/12 x/5 - y = -4/5 (x, y) =

Transcript

00:01 In this problem, we're being asked to solve the given system of equations.

00:04 Now they even gave you a hint in your directions to get rid of our fractions.

00:09 That way it will make our life easier.

00:11 So how do we get rid of fractions in an equation? well, we have to multiply the whole equation by our common denominator.

00:17 So if i'm looking at this first equation, we have denominators of 4, 3, and 12.

00:21 So our common denominator would be 12.

00:23 So i'm gonna multiply the whole equation by 12.

00:25 Well, 12 times negative 3 4ths, 4 goes into 12 three times, so really we're just doing 3 times negative 3x, which would be negative 9x.

00:35 Then i'll bring that 12 again.

00:36 Then we're gonna multiply 12 times y over 3.

00:39 Well, 3 goes into 12 four times, so really we have 4 times y, which is 4y.

00:45 Then if i bring that 12 back, we're gonna multiply 12 by negative 5 over 12.

00:49 Well, 12 goes into 12 one time, so really we're just left with negative 5.

00:55 Alright, so now let's take a look at the second equation.

00:58 We only have two fractions in this case, so what we have to find their common denominator.

01:02 Well, the common denominator for 12 and 5 would be 60.

01:06 So let's go ahead and distribute.

01:07 So first, 60 times negative 5 12ths.

01:10 Well, 12 goes into 60 five times, so 5 times negative 5x would be negative 25x.

01:16 Then we'll bring the 60 back.

01:17 60 times negative y, that's just negative 60y.

01:20 And then we'll have 60 times negative 4 5ths.

01:24 Well, 5 goes into 60 12 times, so 12 times negative 4 would be negative 48.

01:30 Okay, great.

01:30 Now we got rid of the fractions.

01:32 Now we can solve by either elimination or substitution.

01:35 I'm gonna do elimination, meaning that when i add the two equations together, i want one of the variables to cancel out.

01:42 So i'm gonna focus on our y's...

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