Answer:
y = 6
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-x+3y=9\\y = \dfrac{2}{3}x\end{cases}[/tex]
Step 1: Substitute the second equation into the first and solve for x.
[tex]\\\implies -x+3\left(\dfrac{2}{3}x\right)=9\ \textsf{[ Multiply. ]}\\\\\implies -x+2x=9\ \textsf{[ Combine like terms. ]}\\\\\implies \boxed{x=9}[/tex]
Step 2: Substitute 9 as the value of x in any equation and solve for y.
[tex]\\\implies-9+3y=9\ \textsf{[ Add 9 to both sides. ]}\\\\\implies -9+9+3y=9+9\\\\\implies 3y=18\ \textsf{[ Divide both sides by 3. ]}\\\\\implies \dfrac{3y}{3}=\dfrac{18}{3}\\\\\implies \boxed{y=6}[/tex]
The solution to the given system of equations is (9, 6).
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brainly.com/question/27868564
