Solve using elimination. 3x − 3y = –6 5x − 3y = –20 (_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: 3x − 3y = –6 5x − 3y = –20 We can see that the coefficients of y are the same but with opposite signs, so we can eliminate the y variable by subtracting the first equation from the second.Subtract equations: Perform the subtraction of the two equations: (5x − 3y) − (3x − 3y) = (–20) − (–6) This simplifies to: 5x − 3y − 3x + 3y = –20 + 6Simplify equation: Simplify the equation by combining like terms: 5x − 3x = –20 + 6 2x = –14Solve for x: Now, solve for x by dividing both sides of the equation by 2: 2x ÷ 2 = –14 ÷ 2 x = –7Substitute x value: With the value of x found, we can substitute x = –7 into one of the original equations to find the value of y. Let's use the first equation: 3x − 3y = –6 3(–7) − 3y = –6Simplify equation: Perform the multiplication and simplify the equation: –21 − 3y = –6Isolate y term: Add 21 to both sides of the equation to isolate the term with y: –21 + 21 − 3y = –6 + 21 −3y = 15Solve for y: Now, solve for y by dividing both sides of the equation by -3: −3y ÷ (−3) = 15 ÷ (−3) y = –5

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Solve using elimination. $\newline$ $3x - 3y = -6$ $\newline$ $5x - 3y = -20$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

3x - 3y = -6

\newline

5x - 3y = -20

\newline

(_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: $\newline$ $3x − 3y = −6$ $\newline$ $5x − 3y = −20$ $\newline$ We can see that the coefficients of $y$ are the same but with opposite signs, so we can eliminate the $y$ variable by subtracting the first equation from the second.
Subtract equations: Perform the subtraction of the two equations: $\newline$ $(5x − 3y) − (3x − 3y) = (−20) − (−6)$ $\newline$ This simplifies to: $\newline$ $5x − 3y − 3x + 3y = −20 + 6$
Simplify equation: Simplify the equation by combining like terms: $5x - 3x = -20 + 6$ $2x = -14$
Solve for x: Now, solve for x by dividing both sides of the equation by $2$ : $\newline$ $2x \div 2 = -14 \div 2$ $\newline$ $x = -7$
Substitute x value: With the value of x found, we can substitute $x = -7$ into one of the original equations to find the value of y. Let's use the first equation: $\newline$ $3x - 3y = -6$ $\newline$ $3(-7) - 3y = -6$
Simplify equation: Perform the multiplication and simplify the equation: $-21 - 3y = -6$
Isolate y term: Add $21$ to both sides of the equation to isolate the term with $y$ : $\newline$ $-21 + 21 - 3y = -6 + 21$ $\newline$ $-3y = 15$
Solve for y: Now, solve for y by dividing both sides of the equation by $-3$ : $−3y \div (−3) = 15 \div (−3)$ $y = –5$