Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How many solutions does the system of equations below have? $\newline$ $x - 2y - z = 3$ $\newline$ $-2x + 3y - 3z = 0$ $\newline$ $2x + 2y - 3z = 1$ $\newline$ Choices: $\newline$ (A)no solution $\newline$ (B)one solution $\newline$ (C)infinitely many solutions

View step-by-step help

View step-by-step help

Determine the number of solutions to a system of equations in three variables

Full solution

Q. How many solutions does the system of equations below have?

\newline

x - 2y - z = 3

\newline

-2x + 3y - 3z = 0

\newline

2x + 2y - 3z = 1

\newline

Choices:

\newline

(A)no solution

\newline

(B)one solution

\newline

(C)infinitely many solutions

Write Equations: First, let's write down the system of equations: $\newline$ $1$ . $x - 2y - z = 3$ $\newline$ $2$ . $-2x + 3y - 3z = 0$ $\newline$ $3$ . $2x + 2y - 3z = 1$
Eliminate x: Now, let's add equations $1$ and $2$ to eliminate x: $\newline$ $(1) + (2)$ gives us: $\newline$ $x - 2y - z - 2x + 3y - 3z = 3 + 0$ $\newline$ $-x + y - 4z = 3$
Eliminate x Again: Next, let's add equations $1$ and $3$ to eliminate x: $\newline$ $(1) + (3)$ gives us: $\newline$ $x - 2y - z + 2x + 2y - 3z = 3 + 1$ $\newline$ $3x - 4z = 4$
Eliminate y: Now, let's multiply the new equation from step $3$ by $2$ and add it to the new equation from step $4$ to eliminate $y$ : $\newline$ $2(-x + y - 4z) + (3x - 4z) = 2(3) + 4$ $\newline$ $-2x + 2y - 8z + 3x - 4z = 6 + 4$ $\newline$ $x - 12z = 10$

More problems from Determine the number of solutions to a system of equations in three variables

Question

Solve using substitution.

5x - 2y = -7

x = -5

Posted 2 months ago

Question

(1,1)

a solution to this system of equations?

\newline

4x + 10y = 14

\newline

x + 6y = 7

\newline

\newline

\newline

Posted 2 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 2 months ago

Question

Solve using elimination.

\newline

7x - 8y = -17

\newline

-7x + 3y = 2

\newline

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

Posted 2 months ago

Question

\newline

x = -2

\newline

-2x + 2y = -8

\newline

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

Posted 2 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 2 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 2 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 1 month 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 1 month 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 2 months ago