Solve using elimination. 9x − 8y = 11 –8x + 8y = –16 (_____, _____)

Write Equations: First, let's write down the system of equations: 9x − 8y = 11 –8x + 8y = –16 We want to eliminate one of the variables by adding the two equations together. Since the coefficients of y are opposites (−8 and +8), adding the equations will eliminate y.Add Equations: Now, let's add the two equations: (9x − 8y) + (−8x + 8y) = 11 + (−16) This simplifies to: 9x − 8x = 11 − 16Simplify Equation: Next, we perform the subtraction: 1x = −5 This simplifies to: x = −5Substitute x: Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. We'll use the first equation: 9x − 8y = 11 Substitute x = −5: 9(−5) − 8y = 11Solve for x: Perform the multiplication and solve for y: −45 − 8y = 11 Add 45 to both sides: −8y = 11 + 45 −8y = 56Find y: Now, divide both sides by −8 to find y: y = 56 / (−8) y = −7

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve using elimination. $\newline$ $9x - 8y = 11$ $\newline$ $-8x + 8y = -16$ $\newline$ (_, _)

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 = 11

\newline

-8x + 8y = -16

\newline

(_____, _____)

Write Equations: First, let's write down the system of equations: $\newline$ $9x − 8y = 11$ $\newline$ $−8x + 8y = −16$ $\newline$ We want to eliminate one of the variables by adding the two equations together. Since the coefficients of $y$ are opposites ( $−8$ and $+8$ ), adding the equations will eliminate $y$ .
Add Equations: Now, let's add the two equations: $\newline$ $(9x − 8y) + (−8x + 8y) = 11 + (−16)$ $\newline$ This simplifies to: $\newline$ $9x − 8x = 11 − 16$
Simplify Equation: Next, we perform the subtraction: $\newline$ $1x = -5$ $\newline$ This simplifies to: $\newline$ $x = -5$
Substitute $x$ : Now that we have the value of $x$ , we can substitute it back into one of the original equations to find the value of $y$ . We'll use the first equation: $\newline$ $9x - 8y = 11$ $\newline$ Substitute $x = -5$ : $\newline$ $9(-5) - 8y = 11$
Solve for x: Perform the multiplication and solve for y: $\newline$ $-45 - 8y = 11$ $\newline$ Add $45$ to both sides: $\newline$ $-8y = 11 + 45$ $\newline$ $-8y = 56$
Find $y$ : Now, divide both sides by $−8$ to find $y$ :
$y = \frac{56}{(−8)}$
$y = −7$