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monitta
3 years ago
6

Solve the system of equations by substitution. y = 8 X – 2y + 3z = 3 3x + 3y – 2z = 15

Mathematics
1 answer:
Dafna1 [17]3 years ago
6 0

Answer:

Solving systems of equations with 3 variables is very similar to how we solve systems with two variables. When we had two variables we reduced the system down

to one with only one variable (by substitution or addition). With three variables

we will reduce the system down to one with two variables (usually by addition),

which we can then solve by either addition or substitution.

To reduce from three variables down to two it is very important to keep the work

organized. We will use addition with two equations to eliminate one variable.

This new equation we will call (A). Then we will use a different pair of equations

and use addition to eliminate the same variable. This second new equation we

will call (B). Once we have done this we will have two equations (A) and (B)

with the same two variables that we can solve using either method. This is shown

in the following examples.

Example 1.

3x +2y − z = − 1

− 2x − 2y +3z = 5 We will eliminate y using two different pairs of equations

5x +2y − z = 3

Step-by-step explanation:

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\frac{19}{6} many more miles of road are left to build .

<u>Step-by-step explanation:</u>

Here we have , A construction crew must build 4 miles of road in one week. On Monday, they build 1/2 mile of road. On Tuesday, they build 1/3 mile of road.  We need to find that  How many more miles of road are left to build . Let's find out:

  • On Monday, they build 1/2 mile of road.
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Let Miles of road left to build is x So,

⇒ \frac{1}{2} +\frac{1}{3} +x = 4

⇒ x = 4 - (\frac{1}{2} +\frac{1}{3})

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⇒ x = 4 - (\frac{5}{6} )

⇒ x =  (\frac{4(6)-5}{6} )

⇒ x =  \frac{24-5}{6}

⇒ x =  \frac{19}{6}

Therefore, \frac{19}{6} many more miles of road are left to build .

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Answer:

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