Solve using elimination. –5x + 7y = –6 –5x + 4y = 18 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –5x + 7y = –6 –5x + 4y = 18Eliminate x: Since the coefficients of x are the same in both equations, we can eliminate x by subtracting the second equation from the first. Subtract (–5x + 4y = 18) from (–5x + 7y = –6). This gives us: (–5x + 7y) - (–5x + 4y) = (–6) - (18)Find y: Perform the subtraction to eliminate x. –5x + 7y - (–5x) - 4y = –6 - 18 This simplifies to: 7y - 4y = –24Combine Terms: Combine like terms to find the value of y. 7y - 4y = 3y 3y = –24Solve for y: Divide both sides by 3 to solve for y. 3y ÷ 3 = –24 ÷ 3 y = –8Substitute y: Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation: –5x + 7y = –6. Substitute y = –8 into the equation: –5x + 7(–8) = –6.Simplify Equation: Perform the multiplication and simplify the equation. –5x - 56 = –6Isolate x: Add 56 to both sides to isolate the term with x. –5x - 56 + 56 = –6 + 56 –5x = 50Solve for x: Divide both sides by –5 to solve for x. –5x ÷ –5 = 50 ÷ –5 x = –10

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Solve using elimination. $\newline$ $-5x + 7y = -6$ $\newline$ $-5x + 4y = 18$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-5x + 7y = -6

\newline

-5x + 4y = 18

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-5x + 7y = -6$ $\newline$ $-5x + 4y = 18$
Eliminate $x$ : Since the coefficients of $x$ are the same in both equations, we can eliminate $x$ by subtracting the second equation from the first. $\newline$ Subtract $\left( -5x + 4y = 18 \right)$ from $\left( -5x + 7y = -6 \right)$ . $\newline$ This gives us: $\left( -5x + 7y \right) - \left( -5x + 4y \right) = \left( -6 \right) - \left( 18 \right)$
Find $y$ : Perform the subtraction to eliminate $x$ .
$-5x + 7y - (\,-5x) - 4y = \,-6 - 18$
This simplifies to: $7y - 4y = \,-24$
Combine Terms: Combine like terms to find the value of $y$ . $7y - 4y = 3y$ $3y = -24$
Solve for y: Divide both sides by $3$ to solve for y. $\newline$ $3y \div 3 = -24 \div 3$ $\newline$ $y = -8$
Substitute $y$ : Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . Let's use the first equation: $–5x + 7y = –6$ . $\newline$ Substitute $y = –8$ into the equation: $–5x + 7(–8) = –6$ .
Simplify Equation: Perform the multiplication and simplify the equation. $-5x - 56 = -6$
Isolate x: Add $56$ to both sides to isolate the term with $x$ .
$-5x - 56 + 56 = -6 + 56$
$-5x = 50$
Solve for x: Divide both sides by $–5$ to solve for x. $–5x \div –5 = 50 \div –5$ $x = –10$