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{[3x-y=6],[-6x+2y=9]:}

{[(1)/(4)x-(1)/(3)y=(3)/(2)],[(1)/(4)x+(3)/(4)y=(5)/(2)]:}

{[2x-3y+z=7],[x+2y-5z=1],[4y-2z=9]:}

$3$ . $\left\{\begin{array}{c}3 x-y=6 \\ -6 x+2 y=9\end{array}\right.$ $\newline$ $4$ . $\left\{\begin{array}{l}\frac{1}{4} x-\frac{1}{3} y=\frac{3}{2} \\ \frac{1}{4} x+\frac{3}{4} y=\frac{5}{2}\end{array}\right.$ $\newline$ $\left\{\begin{array}{r} 2 x-3 y+z=7 \\ x+2 y-5 z=1 \\ 4 y-2 z=9 \end{array}\right.$

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Set-builder notation

Full solution

Q.

3

.

\left\{\begin{array}{c}3 x-y=6 \\ -6 x+2 y=9\end{array}\right.

\newline

4

.

\left\{\begin{array}{l}\frac{1}{4} x-\frac{1}{3} y=\frac{3}{2} \\ \frac{1}{4} x+\frac{3}{4} y=\frac{5}{2}\end{array}\right.

\newline

\left\{\begin{array}{r} 2 x-3 y+z=7 \\ x+2 y-5 z=1 \\ 4 y-2 z=9 \end{array}\right.

Solve equations: Step $1$ : Solve the first set of equations using elimination method. $\newline$ - Equation $1$ : $3x - y = 6$ $\newline$ - Equation $2$ : $-6x + 2y = 9$ $\newline$ Multiply Equation $1$ by $2$ to align the coefficients of $y$ . $\newline$ - New Equation $1$ : $6x - 2y = 12$ $\newline$ Add Equation $1$ and Equation $2$ : $\newline$ - $6x - 2y + (-6x + 2y) = 12 + 9$ $\newline$ - $0 = 21$

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