Find the solution of the system of equations. {:[-5x+15 y=20],[x+5y=-12]:}

Substitution or Elimination Method: Let's start by solving the system of equations using the substitution or elimination method. The elimination method seems more straightforward since the coefficients of y are multiples of each other. We will multiply the second equation by 3 to make the coefficients of y in both equations equal. Multiplication: 3(x + 5y) = 3(-12) Calculation: 3x + 15y = -36Multiplication and Calculation: Now we have a new system of equations: {:[-5x + 15y = 20],[3x + 15y = -36]:} We will add both equations to eliminate y. Addition: (-5x + 15y) + (3x + 15y) = 20 + (-36) Calculation: -5x + 3x + 15y + 15y = 20 - 36 Simplification: -2x + 30y = -16 However, we made a mistake in simplification; the y terms should cancel out, not add up.

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Find the solution of the system of equations.

{:[-5x+15 y=20],[x+5y=-12]:}

Find the solution of the system of equations. $\newline$ $\begin{aligned} -5 x+15 y & =20 \\ x+5 y & =-12 \end{aligned}$

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Q. Find the solution of the system of equations.

\newline

\begin{aligned} -5 x+15 y & =20 \\ x+5 y & =-12 \end{aligned}

Substitution or Elimination Method: Let's start by solving the system of equations using the substitution or elimination method. The elimination method seems more straightforward since the coefficients of $y$ are multiples of each other. We will multiply the second equation by $3$ to make the coefficients of $y$ in both equations equal. $\newline$ Multiplication: $3(x + 5y) = 3(-12)$ $\newline$ Calculation: $3x + 15y = -36$
Multiplication and Calculation: Now we have a new system of equations: $\newline$ $\begin{cases} -5x + 15y = 20 \ 3x + 15y = -36 \end{cases}$ $\newline$ We will add both equations to eliminate $y$ . $\newline$ Addition: $(-5x + 15y) + (3x + 15y) = 20 + (-36)$ $\newline$ Calculation: $-5x + 3x + 15y + 15y = 20 - 36$ $\newline$ Simplification: $-2x + 30y = -16$ $\newline$ However, we made a mistake in simplification; the $y$ terms should cancel out, not add up.