Problem solving true or false

Question

the point ( 4, 2 ) is a solution of the line 2x-y=6

trueor false

Answer 1

For the point (4,2)

Is it on the line represented by 2x-y=6? The coefficients for this problem are 2 and -1.

The variables are x and y.

For the point (4, 2) x = 4 and y = 2. Applying PEMDAS (Please Excuse My Dear Aunt Sally) - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction - we know we will first multiply the coefficients then do the subtraction.

2(4) = 8 and -1(2) = 6, so 8-6 = 2 and proves that (4,2) is a solution.

Answer 2

Hi Joanna!

The easiest way to solve this kind of problem is to plug in the given point to the equation.

Here are a few similar example problems with solutions:

Is the point (1,3) a solution to the equation y=2x?

Because points are in the form (x,y), we can plug in 1 for x and 3 for y in the equation, so, after we plug in the points, the equation reads (3) = 2(1). Multiplying the right side of the equation out, we get 3 = 2, which is false, so we know that the point (1,3) is not a solution to y = 2x.

Is the point (1,2) a solution to the equation y = 2x?

Same process, just plug in and simplify, then see if the values on either side of the equals sign are equivalent.

y = 2x with (1,2) plugged in is (2) = 2(1). If we simplify the right side of the equation, we get 2 = 2, which is true, so the point (1,2) is a solution to the equation y = 2x.

Now that we've seen some examples, we can undertake the same process for your problem. If we plug in the point (4,2) to 2x - y = 6, we get 2(4) - 2 = 6. Now, just simplify! Does the right side equal the left side? If it does, the answer is true; the point is a solution to the equation. If the right side does not equal the left side, the point is not a solution to the equation.