Solve using elimination. –2x − 5y = 15 –2x − 3y = 1 (_____, _____)

Write Equations: Write down the system of equations. –2x − 5y = 15 –2x − 3y = 1Eliminate x: Since the coefficients of x in both equations are the same but with opposite signs, we can eliminate the x variable by subtracting the second equation from the first. (–2x − 5y) − (–2x − 3y) = 15 − 1Subtract Equations: Perform the subtraction to eliminate the x variable. –2x + 2x − 5y + 3y = 15 − 1Simplify Result: Simplify the resulting equation. 0x − 2y = 14Solve for y: Solve for y. −2y = 14 y = 14 / (−2) y = −7Substitute and Solve: Substitute the value of y back into one of the original equations to solve for x. We can use the second equation for this purpose. –2x − 3(−7) = 1Final Solution: Simplify the equation and solve for x. –2x + 21 = 1 –2x = 1 − 21 –2x = −20 x = −20 / (−2) x = 10

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Solve using elimination. $\newline$ $-2x - 5y = 15$ $\newline$ $-2x - 3y = 1$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-2x - 5y = 15

\newline

-2x - 3y = 1

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-2x - 5y = 15$ $\newline$ $-2x - 3y = 1$
Eliminate $x$ : Since the coefficients of $x$ in both equations are the same but with opposite signs, we can eliminate the $x$ variable by subtracting the second equation from the first. $\newline$ $(–2x − 5y) − (–2x − 3y) = 15 − 1$
Subtract Equations: Perform the subtraction to eliminate the $x$ variable. $\,-2x + 2x - 5y + 3y = 15 - 1$
Simplify Result: Simplify the resulting equation. $\newline$ $0x - 2y = 14$
Solve for y: Solve for y. $\newline$ $-2y = 14$ $\newline$ $y = \frac{14}{(-2)}$ $\newline$ $y = -7$
Substitute and Solve: Substitute the value of $y$ back into one of the original equations to solve for $x$ . We can use the second equation for this purpose. $\newline$ $-2x - 3(-7) = 1$
Final Solution: Simplify the equation and solve for $x$ . $\newline$ $–2x + 21 = 1$ $\newline$ $–2x = 1 − 21$ $\newline$ $–2x = −20$ $\newline$ $x = −20 / (−2)$ $\newline$ $x = 10$