3. Construct Arguments Kavi solved the system of equations as shown. What mistake did Kavi make? What is the correct solution? 3x+4y=33 2x+y=17 y=17-2x 2x+(17-2x)=17 2x+17-2x=17 2x-2x+17=17 17=17 Infinitely many solutions

To determine the mistake Kavi made and find the correct solution, let's analyze the steps Kavi took to solve the system of equations.<br /><br />Given system of equations:<br />$3x + 4y = 33$<br />$2x + y = 17$<br /><br />Kavi's solution:<br />$y = 17 - 2x$<br />$2x + (17 - 2x) = 17$<br />$2x + 17 - 2x = 17$<br />$17 = 17$<br /><br />Kavi's mistake:<br />Kavi correctly substituted the expression for $y$ from the second equation into the first equation. However, he made an error in simplifying the equation. Specifically, he incorrectly simplified $2x + 17 - 2x$ to $17 = 17$, which is not correct.<br /><br />Correct solution:<br />To solve the system of equations correctly, we can use the substitution method again. From the second equation, we have $y = 17 - 2x$. Substituting this expression for $y$ into the first equation, we get:<br /><br />$3x + 4(17 - 2x) = 33$<br /><br />Expanding and simplifying:<br />$3x + 68 - 8x = 33$<br />$-5x + 68 = 33$<br />$-5x = -35$<br />$x = 7$<br /><br />Now, substitute $x = 7$ back into the second equation to find $y$:<br />$2(7) + y = 17$<br />$14 + y = 17$<br />$y = 3$<br /><br />Therefore, the correct solution to the system of equations is $x = 7$ and $y = 3$.