WILL GIVE BRAINLIEST

Mathematics

2 answers:

Alik [6]3 years ago

6 0

Answer:

Divide the second equation $2x+4y=32$ by 2

Step-by-step explanation:

Given a linear equation system, there are three basic operations that we can make in order to obtain a second equivalent system :

1. Making a new equivalent system changing the equations order.

2.Making a new equivalent system multiplying one of the equations by a constant k $(k\neq 0)$ and k ∈ IR

3.Making a new equivalent system adding equations that are a linear combination of the remaining equations.

Examples : The system

$\left \{ {{-x+y=2} \atop {2x+4y=32}} \right.$ is equivalent to

$\left \{ {{2x+4y=32} \atop {-x+y=2}} \right.$ (We used 1.)

The system

$\left \{ {{-x+y=2} \atop {2x+4y=32}} \right.$ is equivalent to $\left \{ {{-10x+10y=20} \atop {2x+4y=32}} \right.$ (We used 2. given that we multiplied the first equation by 10)

The system

- x + y = 2

2 x + 4 y = 32

is equivalent to

- x + y = 2

2 x + 4 y = 32

x + 5 y = 34

(We used 3. given that the third new equation is a linear combination of the first and second equation. The third equation is the sum of the first and the second one)

In the exercise,

$\left \{ {{-x+y=2} \atop {2x+4y=32}} \right.$ is equivalent to

$\left \{ {{-x+y=2} \atop {x+2y=16}} \right.$