Find the solution of the system of equations. {:[x-5y=-24],[5x+10 y=-15]:}

Analyze System: Analyze the system of equations to determine the best method to solve it. The system of equations is: 1) x - 5y = -24 2) 5x + 10y = -15 We can use either substitution or elimination. Since the second equation can be simplified by dividing by 5, we will use elimination after simplifying the second equation.Simplify Second Equation: Simplify the second equation by dividing all terms by 5. 5x + 10y = -15 Divide by 5: x + 2y = -3 Now we have the simplified system: 1) x - 5y = -24 2) x + 2y = -3Eliminate x: Subtract the second equation from the first to eliminate x. (x - 5y) - (x + 2y) = -24 - (-3) This simplifies to: -7y = -21Solve for y: Solve for y. Divide both sides by -7: y = -21 / -7 y = 3Substitute and Solve for x: Substitute the value of y back into one of the original equations to solve for x. Using the first equation: x - 5y = -24 x - 5(3) = -24 x - 15 = -24Solve for x. Add 15 to both sides: x = -24 + 15 x = -9

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Find the solution of the system of equations.

{:[x-5y=-24],[5x+10 y=-15]:}

Find the solution of the system of equations. $\newline$ $\begin{aligned} x-5 y & =-24 \\ 5 x+10 y & =-15 \end{aligned}$

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Q. Find the solution of the system of equations.

\newline

\begin{aligned} x-5 y & =-24 \\ 5 x+10 y & =-15 \end{aligned}

Analyze System: Analyze the system of equations to determine the best method to solve it. $\newline$ The system of equations is: $\newline$ $1$ ) $x - 5y = -24$ $\newline$ $2$ ) $5x + 10y = -15$ $\newline$ We can use either substitution or elimination. Since the second equation can be simplified by dividing by $5$ , we will use elimination after simplifying the second equation.
Simplify Second Equation: Simplify the second equation by dividing all terms by $5$ . $\newline$ $5x + 10y = -15$ $\newline$ Divide by $5$ : $\newline$ $x + 2y = -3$ $\newline$ Now we have the simplified system: $\newline$ $1$ ) $x - 5y = -24$ $\newline$ $2$ ) $x + 2y = -3$
Eliminate x: Subtract the second equation from the first to eliminate x. $\newline$ $(x - 5y) - (x + 2y) = -24 - (-3)$ $\newline$ This simplifies to: $\newline$ $-7y = -21$
Solve for y: Solve for y. $\newline$ Divide both sides by $-7$ : $\newline$ $y = \frac{-21}{-7}$ $\newline$ $y = 3$
Substitute and Solve for x: Substitute the value of $y$ back into one of the original equations to solve for $x$ . Using the first equation: $x - 5y = -24$ $x - 5(3) = -24$ $x - 15 = -24$
Substitute and Solve for $x$ : Substitute the value of $y$ back into one of the original equations to solve for $x$ . Using the first equation: $x - 5y = -24$ $x - 5(3) = -24$ $x - 15 = -24$ Solve for $x$ . Add $15$ to both sides: $x = -24 + 15$ $x = -9$