Solve using elimination. –x − 7y = –13 4x − 7y = 17 (_____, _____)

Write Equations: Write down the system of equations. –x − 7y = –13 4x − 7y = 17Add Equations: Add the two equations together to eliminate the y variable. (–x − 7y) + (4x − 7y) = (–13) + (17) This simplifies to: –x + 4x = 4x – x = 3x −7y − 7y = −14y (This term will be eliminated) –13 + 17 = 4 So, we get: 3x = 4Solve for x: Solve for x. 3x = 4 Divide both sides by 3 to isolate x: x = 4/3Substitute x: Substitute x = 4/3 back into one of the original equations to solve for y. We'll use the first equation: –x − 7y = –13 Substitute x: –(4/3) − 7y = –13Solve for y: Solve for y. Multiply both sides of the equation by 3 to clear the fraction: –3*(4/3) − 3*7y = –3*13 This simplifies to: –4 − 21y = –39 Now, add 4 to both sides: −21y = –39 + 4 −21y = –35 Now, divide both sides by -21 to solve for y: y = –35 / -21 y = 35 / 21 y = 5/3

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Solve using elimination. $\newline$ $-x - 7y = -13$ $\newline$ $4x - 7y = 17$ $\newline$ (_, _)

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Precalculus

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-x - 7y = -13

\newline

4x - 7y = 17

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-x - 7y = -13$ $\newline$ $4x - 7y = 17$
Add Equations: Add the two equations together to eliminate the $y$ variable. $\newline$ $(-x - 7y) + (4x - 7y) = (-13) + (17)$ $\newline$ This simplifies to: $\newline$ $-x + 4x = 4x - x = 3x$ $\newline$ $-7y - 7y = -14y$ (This term will be eliminated) $\newline$ $-13 + 17 = 4$ $\newline$ So, we get: $\newline$ $3x = 4$
Solve for x: Solve for x. $\newline$ $3x = 4$ $\newline$ Divide both sides by $3$ to isolate $x$ : $\newline$ $x = \frac{4}{3}$
Substitute $x$ : Substitute $x = \frac{4}{3}$ back into one of the original equations to solve for $y$ . We'll use the first equation: $\newline$ $–x − 7y = –13$ $\newline$ Substitute $x$ : $\newline$ $–\left(\frac{4}{3}\right) − 7y = –13$
Solve for y: Solve for y. $\newline$ Multiply both sides of the equation by $3$ to clear the fraction: $\newline$ $-3*(\frac{4}{3}) - 3*7y = -3*13$ $\newline$ This simplifies to: $\newline$ $-4 - 21y = -39$ $\newline$ Now, add $4$ to both sides: $\newline$ $-21y = -39 + 4$ $\newline$ $-21y = -35$ $\newline$ Now, divide both sides by $-21$ to solve for y: $\newline$ $y = \frac{-35}{-21}$ $\newline$ $y = \frac{35}{21}$ $\newline$ $y = \frac{5}{3}$