Solve using elimination. –3x + y = –17 –3x + 7y = 7 (_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. –3x + y = –17 –3x + 7y = 7Eliminate x: Since the coefficients of x in both equations are the same, we can eliminate the x variable by subtracting the second equation from the first. Subtract the second equation from the first: (–3x + y) - (–3x + 7y) = –17 - 7Subtract Equations: Perform the subtraction to eliminate the x variable. –3x + y + 3x - 7y = –17 - 7 y - 7y = –17 - 7 -6y = –24Solve for y: Solve for y by dividing both sides of the equation by -6. -6y / -6 = –24 / -6 y = 4Substitute y: Substitute the value of y back into one of the original equations to solve for x. We can use the first equation for this purpose. –3x + y = –17 –3x + 4 = –17Solve for x: Solve for x by adding -4 to both sides of the equation and then dividing by -3. –3x = –17 - 4 –3x = –21 x = –21 / -3 x = 7

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Solve using elimination. $\newline$ $-3x + y = -17$ $\newline$ $-3x + 7y = 7$ $\newline$ (_, _)

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Grade 8

Solve a system of equations using elimination

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Q. Solve using elimination.

\newline

-3x + y = -17

\newline

-3x + 7y = 7

\newline

(_____, _____)

Write Equations: Write down the system of equations to be solved using elimination. $\newline$ $-3x + y = -17$ $\newline$ $-3x + 7y = 7$
Eliminate $x$ : Since the coefficients of $x$ in both equations are the same, we can eliminate the $x$ variable by subtracting the second equation from the first. $\newline$ Subtract the second equation from the first: $\newline$ $(–3x + y) - (–3x + 7y) = –17 - 7$
Subtract Equations: Perform the subtraction to eliminate the $x$ variable. $\newline$ $-3x + y + 3x - 7y = -17 - 7$ $\newline$ $y - 7y = -17 - 7$ $\newline$ $-6y = -24$
Solve for y: Solve for y by dividing both sides of the equation by -6＂).$\newline\$-6y / -6 = -24 / -6$$\newline$$y = 4$
Substitute $y$: Substitute the value of $y$ back into one of the original equations to solve for $x$. We can use the first equation for this purpose.$\newline$$–3x + y = –17$$\newline$$–3x + 4 = –17$
Solve for x: Solve for x by adding $-4$ to both sides of the equation and then dividing by $-3$.$\newline$$-3x = -17 - 4$$\newline$$-3x = -21$$\newline$$x = -21 / -3$$\newline$$x = 7$