Question

Which ordered pair is a solution of the equation?

3x+3y= -x+5y

a) only (1,2)
b) only (2,4)
c) both (1,2) and (2,4)
d) neither

Answer 1

Both ordered pairs (1,2) and (2,4) are solutions to the equation 3x+3y=-x+5y, which simplifies to 2x=y. Thus, the correct answer is c) both (1,2) and (2,4).

Step-by-step explanation:

To determine which ordered pair is a solution to the equation 3x+3y=-x+5y, we can substitute the x and y values from each ordered pair into the equation to see if it makes the equation true. Let's first simplify the equation by moving all terms involving variables to one side and combining like terms.

Add x to both sides: 4x + 3y = 5y

Subtract 3y from both sides: 4x = 2y

Divide both sides by 2: 2x = y

Now, let's test the ordered pairs:

For the ordered pair (1, 2): 2x = y becomes 2(1) = 2, which is true.

For the ordered pair (2, 4): 2x = y becomes 2(2) = 4, which is also true.

Therefore, both ordered pairs are solutions to the equation. The correct answer is c) both (1,2) and (2,4).

Answer 2

First simplify the equation.

3x+3y= -x+5y

4x=2y

2x=y

y=2x

Means that the y value is 2 times the x value.

answer: C but there are more solutions than just (1,2) and (2,4)