Solve using elimination. 3x − 7y = 1 5x − 7y = –3 (_____, _____)

Write System of Equations: Write down the system of equations to identify the strategy for elimination. 3x − 7y = 1 5x − 7y = –3 We can subtract one equation from the other to eliminate the y variable because the coefficients of y are the same in both equations.Subtract Equations: Subtract the first equation from the second equation to eliminate the y variable. (5x − 7y) − (3x − 7y) = (–3) − (1) 5x − 3x − 7y + 7y = –3 − 1 2x = –4Solve for x: Solve for x by dividing both sides of the equation by 2. 2x ÷ 2 = –4 ÷ 2 x = –2Substitute x: Substitute x = –2 back into one of the original equations to solve for y. Using the first equation: 3x − 7y = 1 3(–2) − 7y = 1 –6 − 7y = 1Add to Isolate y: Add 6 to both sides of the equation to isolate the term with y. –6 + 6 − 7y = 1 + 6 −7y = 7Divide to Solve y: Divide both sides of the equation by -7 to solve for y. −7y ÷ (−7) = 7 ÷ (−7) y = –1

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Solve using elimination. $\newline$ $3x - 7y = 1$ $\newline$ $5x - 7y = -3$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

3x - 7y = 1

\newline

5x - 7y = -3

\newline

(_____, _____)

Write System of Equations: Write down the system of equations to identify the strategy for elimination. $\newline$ $3x − 7y = 1$ $\newline$ $5x − 7y = −3$ $\newline$ We can subtract one equation from the other to eliminate the $y$ variable because the coefficients of $y$ are the same in both equations.
Subtract Equations: Subtract the first equation from the second equation to eliminate the $y$ variable. $\newline$ $(5x − 7y) − (3x − 7y) = (–3) − (1)$ $\newline$ $5x − 3x − 7y + 7y = –3 − 1$ $\newline$ $2x = –4$
Solve for x: Solve for x by dividing both sides of the equation by $2$ . $\newline$ $2x \div 2 = -4 \div 2$ $\newline$ $x = -2$
Substitute x: Substitute $x = -2$ back into one of the original equations to solve for $y$ . Using the first equation: $3x - 7y = 1$ $3(-2) - 7y = 1$ $-6 - 7y = 1$
Add to Isolate y: Add $6$ to both sides of the equation to isolate the term with $y$ . $\newline$ $-6 + 6 - 7y = 1 + 6$ $\newline$ $-7y = 7$
Divide to Solve $y$ : Divide both sides of the equation by $-7$ to solve for $y$ . $\frac{-7y}{(-7)} = \frac{7}{(-7)}$ $y = -1$