Write a system of equations where the sum of two numbers is 10 and the difference is 6. Can you determine the solution without graphing? Guess and check.

Answer 1

Let's call the two numbers $x$ and $y$. We are given that the sum of the two numbers is 10, so we can write the equation $x+y=10$. We are also given that the difference between the two numbers is 6, so we can write the equation $x-y=6$.

We can solve this system of equations by adding the two equations together to eliminate $y$. Adding the left sides gives $x+y$, and adding the right sides gives $10+6=16$. So our equation is $x+y=16$.

If we subtract the second equation from the first equation, we can eliminate $y$ again. Subtracting the left sides gives $x-y$, and subtracting the right sides gives $6-10=-4$. So our equation is $x-y=-4$.

We have now reduced the system of equations to a single equation: $x+y=16$ and $x-y=-4$. To solve for $x$ and $y$, we can add the two equations together to eliminate $y$: $(x+y)+(x-y)=16+(-4)$. Simplifying the left side gives $2x$, and simplifying the right side gives $12$. So our equation is $2x=12$.

Dividing both sides of the equation by 2 gives $x=\frac{12}{2}=6$. Plugging this value of $x$ into either of the original equations, we find $y=10-x=10-6=4$.

So the solution to the system of equations is $x=6$ and $y=4$.

Answer 2

How is that correct if the equation x-y=6
Has to = 6
6-4=2 NOT 6

Answer 3

???