Subject: common solution

Name: Samantha

Who is asking: Student Level: Middle


  1. Solve for common solution: x+y=6 2x-3y=2

  2. Solve for y in terms of x: 3x-y=4
Hi Samantha,

For the first problem think of (x,y) as a fixed point that is on both graphs, x+y=6 and 2x-3y=2. Since (x,y) is on the first graph the numbers x and y are related by x+y=6. Subtracting x from both sides this relationship becomes y = 6 - x.

Since (x,y) is also on the graph of the second equation the numbers x and y satisify the second equation 2x-3y=2. But we know that y = 6 - x and hence

2x - 3(6 - x) = 2 Simplify this expression and solve for x. Once you know x you can find y since y = 6 - x.

For the second problem you are looking for an expression that is equivalent to 3x - y = 4 which is of the form

y = some expression that doesn't involve y. If you subtract 3x from both sides of the expression 3x - y = 4 you get 3x - y -3x = 4 - 3x


-y = 4 - 3x
Multiplying both sides by -1 gives y = 3x - 4

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