Answered

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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.

Sagot :

skzmakemestay

answer (in words)

FALSE. the coordinate pair (5, 2) is not a solution to the equation [tex]2x+3y=10[/tex]. in order to figure out whether or not the statement is true or false, plug the [tex]x[/tex] and [tex]y[/tex] values from the coordinate pair (5, 2) into the given equation, [tex]2x+3y=10[/tex]. 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 [tex]x[/tex] in the equation [tex]2x+3y=10[/tex].

  • [tex]2x+3y=10[/tex] ⇒ [tex]2(5)+3y=10[/tex]

then plug in 2 for [tex]y[/tex].

  • [tex]2(5)+3y=10[/tex] ⇒ [tex]2(5)+3(2)=10[/tex]

now your equation is [tex]2(5)+3(2)=10[/tex]. 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.

  • [tex]2(5)+3(2)=10[/tex] ⇒ [tex]10 + 3(2) = 10[/tex]

multiply 3 · 2.

  • [tex]10 + 3(2) = 10[/tex] ⇒ [tex]10 + 6 = 10[/tex]

add 10 + 6.

  • [tex]10 + 6 = 10[/tex] ⇒ [tex]16=10[/tex]

16 and 10 are not equal, therefore (5, 2) is not a solution to the equation [tex]2x+3y=10[/tex]. 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

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