Math / Algebra

QuestionUse technology to find the solution of the following system. $\begin{aligned} 1.8 x-0.3 y+2.7 z & =4.89 \\ 3.3 x-5.6 y+7.5 z & =13.55 \\ 1.6 y+5.32 & =3.3 z-0.4 x \end{aligned}$
The solution set is $\square$ $\square$ $\square$ (Simplify your answers. Type integers or decimals.)

Studdy Solution

STEP 1

What is this asking? We need to solve a system of three equations with three unknown variables: $x$ , $y$ , and $z$ .
Basically, we're looking for the magic values of $x$ , $y$ , and $z$ that make all three equations true at the same time! Watch out! Be super careful when rearranging the equations!
It's easy to make a sign error, which will throw everything off.
Also, make sure you enter the values for $x$ , $y$ , and $z$ in the correct boxes at the end!

STEP 2

1. Rewrite the equations
2. Use technology to solve

STEP 3

We want to make sure our equations are in a standard format, which will make it easier for our technology (calculator or software) to understand them.
The standard format is $Ax + By + Cz = D$ , where $A$ , $B$ , $C$ , and $D$ are constants.

STEP 4

The third equation, $1.6y + 5.32 = 3.3z - 0.4x$ , needs a little rearranging.
Let's move all the variables to the left side and the constant to the right side.
We can do this by adding $0.4x$ to both sides and subtracting $3.3z$ from both sides, and we get $0.4x + 1.6y - 3.3z = -5.32$ .
Now it's in the standard format!

STEP 5

So, our system of equations now looks like this: $\begin{cases} 1.8x - 0.3y + 2.7z = 4.89 \\ 3.3x - 5.6y + 7.5z = 13.55 \\ 0.4x + 1.6y - 3.3z = -5.32 \end{cases}$

STEP 6

Now, we can use a calculator or software that can solve systems of equations.
There are many options available, such as graphing calculators, online calculators, or computer software.
Pick your favorite!

STEP 7

Enter the coefficients of the equations into your chosen technology.
Double-check everything to make sure you've entered the numbers correctly!
Even a small typo can lead to a wrong answer.

STEP 8

Let the technology do the heavy lifting!
Press the "solve" button or equivalent, and the calculator or software will find the values of $x$ , $y$ , and $z$ that satisfy all three equations.

STEP 9

The solution we get is $x = \textbf{0.3}$ , $y = \textbf{2.7}$ , and $z = \textbf{2.4}$ .

STEP 10

$x = 0.3$ $y = 2.7$ $z = 2.4$

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QuestionUse technology to find the solution of the following system. $\begin{aligned} 1.8 x-0.3 y+2.7 z & =4.89 \\ 3.3 x-5.6 y+7.5 z & =13.55 \\ 1.6 y+5.32 & =3.3 z-0.4 x \end{aligned}$
The solution set is $\square$ $\square$ $\square$ (Simplify your answers. Type integers or decimals.)

Studdy Solution

STEP 1

STEP 2

1. Rewrite the equations
2. Use technology to solve

STEP 3

We want to make sure our equations are in a standard format, which will make it easier for our technology (calculator or software) to understand them.
The standard format is $Ax + By + Cz = D$ , where $A$ , $B$ , $C$ , and $D$ are constants.

STEP 4

STEP 5

So, our system of equations now looks like this: $\begin{cases} 1.8x - 0.3y + 2.7z = 4.89 \\ 3.3x - 5.6y + 7.5z = 13.55 \\ 0.4x + 1.6y - 3.3z = -5.32 \end{cases}$

STEP 6

Now, we can use a calculator or software that can solve systems of equations.
There are many options available, such as graphing calculators, online calculators, or computer software.
Pick your favorite!

STEP 7

Enter the coefficients of the equations into your chosen technology.
Double-check everything to make sure you've entered the numbers correctly!
Even a small typo can lead to a wrong answer.

STEP 8

Let the technology do the heavy lifting!
Press the "solve" button or equivalent, and the calculator or software will find the values of $x$ , $y$ , and $z$ that satisfy all three equations.

STEP 9

The solution we get is $x = \textbf{0.3}$ , $y = \textbf{2.7}$ , and $z = \textbf{2.4}$ .

STEP 10

$x = 0.3$ $y = 2.7$ $z = 2.4$

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Studdy Solution

STEP 1

STEP 2

1. Rewrite the equations2. Use technology to solve

STEP 3

We want to make sure our equations are in a standard format, which will make it easier for our technology (calculator or software) to understand them.The standard format is Ax+By+Cz=DAx + By + Cz = DAx+By+Cz=D, where AAA, BBB, CCC, and DDD are constants.

STEP 4

STEP 5

STEP 6

Now, we can use a calculator or software that can solve systems of equations.There are many options available, such as graphing calculators, online calculators, or computer software.Pick your favorite!

STEP 7

Enter the coefficients of the equations into your chosen technology.Double-check everything to make sure you've entered the numbers correctly!Even a small typo can lead to a wrong answer.

STEP 8

Let the technology do the heavy lifting!Press the "solve" button or equivalent, and the calculator or software will find the values of xxx, yyy, and zzz that satisfy all three equations.

STEP 9

The solution we get is x=0.3x = \textbf{0.3}x=0.3, y=2.7y = \textbf{2.7}y=2.7, and z=2.4z = \textbf{2.4}z=2.4.

STEP 10

x=0.3x = 0.3x=0.3 y=2.7y = 2.7y=2.7 z=2.4z = 2.4z=2.4

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Rewrite the equations
2. Use technology to solve

We want to make sure our equations are in a standard format, which will make it easier for our technology (calculator or software) to understand them.
The standard format is $Ax + By + Cz = D$ , where $A$ , $B$ , $C$ , and $D$ are constants.

Now, we can use a calculator or software that can solve systems of equations.
There are many options available, such as graphing calculators, online calculators, or computer software.
Pick your favorite!

Enter the coefficients of the equations into your chosen technology.
Double-check everything to make sure you've entered the numbers correctly!
Even a small typo can lead to a wrong answer.

Let the technology do the heavy lifting!
Press the "solve" button or equivalent, and the calculator or software will find the values of $x$ , $y$ , and $z$ that satisfy all three equations.

The solution we get is $x = \textbf{0.3}$ , $y = \textbf{2.7}$ , and $z = \textbf{2.4}$ .

$x = 0.3$ $y = 2.7$ $z = 2.4$