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