So, I've got these other sets of problems, that are telling me to write equivilant equations for the equations given, heres what I think.
1) x+y=-10
-5+5=10
-5(2)+10
2) 5x+10y=15
5x(3)=15
5x+10=15
3)-x+2y=9
y=3(3)=9
3+6=9
Heres what I need YOU tutors to help me with:
Could you tell me if my answers are correct, if not explain why?
Thank you.
I think you are totally wrong.
Take the last one.
-x+2y=9
here are some equivalent equations:
2y-9=x
x+9=2y
14y=63+7x
Equivalent equations are equations that have the same solution.
Okay, thank you.
Let's go through each of your answers and check if they are correct.
1) x+y=-10
To write an equivalent equation, you need to perform the same operation on both sides of the equation. However, in your first step, you seem to have made an error. Adding 5 to both sides of the equation should give you:
x + y + 5 = -10 + 5
x + y + 5 = -5
2) 5x + 10y = 15
In this equation, you need to isolate the terms involving variables on one side. In your step, you multiplied both sides by 3, but that is not a correct operation. To write an equivalent equation, you need to divide both sides by 5:
(5x + 10y)/5 = 15/5
x + 2y = 3
3) -x + 2y = 9
To rewrite it as an equivalent equation, you need to find the value of x in terms of y or vice versa. Your step shows y = 3(3) = 9, which is incorrect. To solve for y, you need to isolate the y-term:
-x + 2y = 9
2y = 9 + x
y = (9 + x)/2
In summary, your answers are not correct. The correct equivalent equations are:
1) x + y + 5 = -5
2) x + 2y = 3
3) y = (9 + x)/2
Let's go through each set of problems and check if your answers are correct:
1) The original equation is x + y = -10. To write an equivalent equation, you need to perform the same operation on both sides of the equation. In this case, you can add 10 to both sides to move the -10 to the right side:
x + y + 10 = -10 + 10
x + y + 10 = 0
Your answer of -5 + 5 = 10 is incorrect because it is not equivalent to the original equation. Similarly, your answer of -5(2) + 10 is incorrect as well.
2) The original equation is 5x + 10y = 15. To write an equivalent equation, you can divide both sides of the equation by 5 to simplify it:
5x/5 + 10y/5 = 15/5
x + 2y = 3
Your answer of 5x(3) = 15 is incorrect. It seems like you tried to multiply the equation by 3, but that is not a valid operation for writing an equivalent equation.
3) The original equation is -x + 2y = 9. To write an equivalent equation, you can multiply both sides of the equation by -1 to change the sign of each term:
-1*(-x + 2y) = -1*9
x - 2y = -9
Your answer of y = 3(3) = 9 is incorrect. You cannot substitute a number for a variable in order to write an equivalent equation. Similarly, your answer of 3 + 6 = 9 is incorrect.
So, none of your answers are correct for the given equations. To write equivalent equations, you need to perform valid operations on both sides while maintaining the equality between them.