Solve using elimination. x + 5y = –12 x − 4y = –3 (_____, _____)

Align Equations for Elimination: Align the equations for elimination. Given equations: 1) x + 5y = –12 2) x − 4y = –3 We aim to eliminate x by making the coefficients of x equal in both equations. Multiply Equations for Alignment: Multiply the first equation by 1 and the second equation by -1 to align the coefficients of x for elimination. 1) x + 5y = -12 (multiplied by 1) 2) -x + 4y = 3 (multiplied by -1) Now, add these two equations together. Add Modified Equations: Add the modified equations. (x + 5y) + (-x + 4y) = -12 + 3 Combine like terms: 5y + 4y = -9 9y = -9 Now, solve for y by dividing both sides by 9. y = -9 / 9 y = -1 Solve for y: Substitute y = -1 back into one of the original equations to find x. Use the first equation: x + 5(-1) = -12 x - 5 = -12 Now, solve for x by adding 5 to both sides. x = -12 + 5 x = -7

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Solve using elimination. $\newline$ $x + 5y = -12$ $\newline$ $x - 4y = -3$ $\newline$ (_, _)

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Precalculus

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

x + 5y = -12

\newline

x - 4y = -3

\newline

(_____, _____)

Align Equations for Elimination: Align the equations for elimination. $\newline$ Given equations: $\newline$ $1$ ) $x + 5y = -12$ $\newline$ $2$ ) $x - 4y = -3$ $\newline$ We aim to eliminate $x$ by making the coefficients of $x$ equal in both equations.
Multiply Equations for Alignment: Multiply the first equation by $1$ and the second equation by $-1$ to align the coefficients of $x$ for elimination. $\newline$ $1$ ) $x + 5y = -12$ (multiplied by $1$ ) $\newline$ $2$ ) $-x + 4y = 3$ (multiplied by $-1$ ) $\newline$ Now, add these two equations together.
Add Modified Equations: Add the modified equations. $\newline$ $(x + 5y) + (-x + 4y) = -12 + 3$ $\newline$ Combine like terms: $\newline$ $5y + 4y = -9$ $\newline$ $9y = -9$ $\newline$ Now, solve for y by dividing both sides by $9$ . $\newline$ $y = -9 / 9$ $\newline$ $y = -1$
Solve for $y$ : Substitute $y = -1$ back into one of the original equations to find $x$ . Use the first equation: $x + 5(-1) = -12$ $x - 5 = -12$ Now, solve for $x$ by adding $5$ to both sides. $x = -12 + 5$ $x = -7$