Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve using elimination. $\newline$ $-8x + 9y = 12$ $\newline$ $-9x + 9y = 9$ $\newline$ (_, _)

View step-by-step help

View step-by-step help

Solve a system of equations using elimination

Full solution

Q. Solve using elimination.

\newline

-8x + 9y = 12

\newline

-9x + 9y = 9

\newline

(_____, _____)

Write Equations: Write down the system of equations. $\newline$ $-8x + 9y = 12$ $\newline$ $-9x + 9y = 9$
Elimination Method: To use elimination, we want to eliminate one of the variables by adding or subtracting the equations. Since the coefficients of $y$ are the same, we can subtract the second equation from the first to eliminate $y$ . $\newline$ Subtract the second equation from the first: $\newline$ $(–8x + 9y) - (–9x + 9y) = 12 - 9$
Subtract Equations: Perform the subtraction. $\newline$ $-8x + 9y + 9x - 9y = 12 - 9$
Simplify Result: Simplify the equation. $\newline$ $x = 3$
Substitute $x$ Value: Now that we have the value of $x$ , we can substitute it back into one of the original equations to find the value of $y$ . Let's use the first equation: $\newline$ $–8x + 9y = 12$ $\newline$ Substitute $x = 3$ into the equation: $\newline$ $–8(3) + 9y = 12$
Solve for y: Perform the multiplication and solve for y. $-24 + 9y = 12$
Isolate y Term: Add $24$ to both sides of the equation to isolate the term with $y$ . $\newline$ $9y = 12 + 24$
Divide to Solve $y$ : Perform the addition. $9y = 36$
Calculate Final y Value: Divide both sides by $9$ to solve for y. $\newline$ $y = \frac{36}{9}$
Calculate Final y Value: Divide both sides by $9$ to solve for y. $\newline$ y = $\frac{36}{9}$ Calculate the value of y. $\newline$ y = $4$

More problems from Solve a system of equations using elimination

Question

Solve using substitution.

5x - 2y = -7

x = -5

Posted 3 months ago

Question

(1,1)

a solution to this system of equations?

\newline

4x + 10y = 14

\newline

x + 6y = 7

\newline

\newline

\newline

Posted 3 months ago

Question

Which describes the system of equations below?

\newline

y = –3x + 9

\newline

y = –3x + 9

\newline

\newline

\text{(A) consistent and independent}

\newline

\text{(B) consistent and dependent}

\newline

\text{(C) inconsistent}

Posted 3 months ago

Question

Solve using elimination.

\newline

7x - 8y = -17

\newline

-7x + 3y = 2

\newline

(\_\_\_\_, \_\_\_\_)

Posted 3 months ago

Question

\newline

x = -2

\newline

-2x + 2y = -8

\newline

(\_\_\_\_, \_\_\_\_)

Posted 3 months ago

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

At a community barbecue, Mrs. Wilkerson and Mr. Hogan are buying dinner for their families. Mrs. Wilkerson purchases

3

hot dog meals and

3

hamburger meals, paying a total of

\$36

. Mr. Hogan buys

1

hot dog meal and

3

hamburger meals, spending

\$26

in all. How much do the meals cost?

\newline

Hot dog meals cost

\$

_______ each, and hamburger meals cost

\$

Posted 3 months ago

Question

Solve the system of equations by substitution.

\newline

-3x - y - 3z = -11

\newline

z = 5

\newline

x - y + 3z = 19

\newline

(____.____,____)

Posted 3 months ago

Question

Solve the system of equations by elimination.

\newline

x - 3y - 2z = 10

\newline

3x + 2y + 2z = 14

\newline

2x - 3y - 2z = 16

\newline

(\_,\_,\_)

Posted 2 months ago

Question

Solve the system of equations.

\newline

y = x^2 + 36x + 3

\newline

y = 22x - 37

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(\_,\_)

\newline

(\_,\_)

Posted 2 months ago

Question

Solve the system of equations.

\newline

y = -x - 24

\newline

x^2 + y^2 = 488

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(\_,\_)

\newline

(\_,\_)

Posted 3 months ago