Does this equation have more than one solution?

Question

x+y=10

x+y=12

Is there infinitely many solutions or only one?

Answer 1

The graphs of these 2 equations are parallel; therefore, there are no solutions.

Answer 2

Does this equation have more than one solution? x + y = 10 & x + y = 12. Is there infinitely many solutions or only one?

Detailed Answer:

In Mathematics, common sense is extremely important. With that said, let me ask you a question: Can the same thing be 10 and 12 at the same time? Specific to this question: Can the same “x + y” be equal to 10 and 12 at the same time? Absolutely – Not (that is common sense is extremely important). Therefore, x + y = 10 & x + y = 12 is the same as saying: 10 = 12 which is Absolutely Non-Sense = False.  Therefore, the answer is: No Solution

Here the solution:

x + y = 10 ==> Equation 1

x + y = 12 ==> Equation 2

Subtract Equation 1 from Equation 2

Equation 2 – Equation 1 ==> (x + y = 12) – (x + y = 10) ==> (x – x + y – y = 12 – 10) ==> (0 + 0 = 2) ==> 0 = 2 (Means – No Solution)

Answer 3

Hi Anna!

Did you write the question correctly? Because to find "a solution," I would have eliminated one variable and worked with the other variable before concluding the values of each variable.

If I want to work with the y-variable first, I have eliminated the x-variable, then work with the y-variable. Once I get a number, I can then find what the x-variable is by substituting the value of the y-variable into the equation to see what x is.

However, my other concern is that if you have 2 of the same variables added together, how does that equal two different numbers. For example, if we look at the first equation, x+y=10. I can say that x = 5 and y = 5, so 5+5 = 10. But for the second equation 5+5 =/ (not equal to) 12.

Same goes for if I started with the second equation,where x = 5 and y = 7. 5+7 = 12, but substituting that into the first equation will give me 5+7 =/ (not equal to) 10.

Please relook at the question and correct any mistakes, if needed!

Answer 4

There are infinitely many solutions because both equations yield lines with a slope of -1. This means the lines are parallel to each other, and will never intersect.

To visualize this, enter both equations into a graphing calculator or in desmos (https://www.desmos.com/calculator). You should see two parallel lines.