Question

True or false? A correct answer is worth (2 pts). Explain how you know for the additional (2 pts). Using complete sentence for (1 pts)

(5,2) is a solution to the equation 2x + 3y = 10.

Answer 1

answer (in words)

FALSE. the coordinate pair (5, 2) is not a solution to the equation
`2x+3y=10`. in order to figure out whether or not the statement is true or false, plug the
`x` and
`y` values from the coordinate pair (5, 2) into the given equation,
`2x+3y=10`. if both sides of the equation end up equal, the coordinate pair is a solution to the equation. if not, the coordinate pair is not a solution to that equation.

(i hope i explained that well enough, i'm better at explaining it algebraically as opposed to putting it into words lol)

answer (algebraic/steps for solving)

first, plug in 5 for
`x` in the equation
`2x+3y=10`.

• 
  `2x+3y=10` ⇒
  `2(5)+3y=10`

then plug in 2 for
`y`.

• 
  `2(5)+3y=10` ⇒
  `2(5)+3(2)=10`

now your equation is
`2(5)+3(2)=10`. all that's left to do is to simplify. you can do this in whatever order you'd like, but i'll start with multiplying 2 · 5.

• 
  `2(5)+3(2)=10` ⇒
  `10 + 3(2) = 10`

multiply 3 · 2.

• 
  `10 + 3(2) = 10` ⇒
  `10 + 6 = 10`

add 10 + 6.

• 
  `10 + 6 = 10` ⇒
  `16=10`

16 and 10 are not equal, therefore (5, 2) is not a solution to the equation
`2x+3y=10`. in order for a coordinate pair to be the solution to an equation, both sides of the equation need to end up equal after solving and simplifying.

i hope this helps! have a great rest of your day <3