Solve using elimination. –9x − 8y = –18 –9x − 9y = –9 (_____, _____)

Write Equations: Write down the system of equations. –9x − 8y = –18 –9x − 9y = –9Eliminate Variable: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of x are the same in both equations, we can subtract the second equation from the first to eliminate x. Subtract the second equation from the first: (–9x − 8y) − (–9x − 9y) = (–18) − (–9)Subtract Equations: Perform the subtraction. –9x + 9x − 8y + 9y = –18 + 9 0x + y = –9 This simplifies to: y = –9Substitute y: Now that we have the value of y, we can substitute it into one of the original equations to find the value of x. Let's use the first equation: –9x − 8y = –18 Substitute y = –9 into the equation: –9x − 8(–9) = –18Solve for x: Solve for x. –9x + 72 = –18 Add 18 to both sides: –9x + 72 + 18 = –18 + 18 –9x + 90 = 0 Subtract 90 from both sides: –9x = –90 Divide by –9: x = 10Find Solution: We have found the values of x and y. x = 10, y = –9 These values are the solution to the system of equations.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve using elimination. $\newline$ $-9x - 8y = -18$ $\newline$ $-9x - 9y = -9$ $\newline$ (_, _)

View step-by-step help

Home

Math Problems

Grade 8

Solve a system of equations using elimination

Full solution

Q. Solve using elimination.

\newline

-9x - 8y = -18

\newline

-9x - 9y = -9

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-9x - 8y = -18$ $\newline$ $-9x - 9y = -9$
Eliminate Variable: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of $x$ are the same in both equations, we can subtract the second equation from the first to eliminate $x$ . Subtract the second equation from the first: $(–9x − 8y) − (–9x − 9y) = (–18) − (–9)$
Subtract Equations: Perform the subtraction. $\newline$ $-9x + 9x - 8y + 9y = -18 + 9$ $\newline$ $0x + y = -9$ $\newline$ This simplifies to: $\newline$ $y = -9$
Substitute $y$ : Now that we have the value of $y$ , we can substitute it into one of the original equations to find the value of $x$ . Let's use the first equation: $\newline$ $–9x − 8y = –18$ $\newline$ Substitute $y = –9$ into the equation: $\newline$ $–9x − 8(–9) = –18$
Solve for x: Solve for x. $\newline$ $-9x + 72 = -18$ $\newline$ Add $18$ to both sides: $\newline$ $-9x + 72 + 18 = -18 + 18$ $\newline$ $-9x + 90 = 0$ $\newline$ Subtract $90$ from both sides: $\newline$ $-9x = -90$ $\newline$ Divide by $-9$ : $\newline$ $x = 10$
Find Solution: We have found the values of $x$ and $y$ . $x = 10$ , $y = -9$ These values are the solution to the system of equations.