Question

Doy corona y gracias!!
Completa las siguientes frases con el vocabulario de los sistemas de ecuaciones en ingles.
- A linear equation whit two ____ is a linear equation.
- A linear ____ is an equuation of degree 1 whit one or more unknows.
- A solution of a linear equiation whit two unkonws is a pair of values, one for each unknow, thath make the ____ true.
- Two linear equations are equivalent if they have the same ____.
Gracias!

Answer 1

Respuesta:

In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.[1][2][3][4][5] For example,

A linear system in three variables determines a collection of planes. The intersection point is the solution.

{\displaystyle {\begin{alignedat}{7}3x&&\;+\;&&2y&&\;-\;&&z&&\;=\;&&1&\\2x&&\;-\;&&2y&&\;+\;&&4z&&\;=\;&&-2&\\-x&&\;+\;&&{\tfrac {1}{2}}y&&\;-\;&&z&&\;=\;&&0&\end{alignedat}}} {\begin{alignedat}{7}3x&&\;+\;&&2y&&\;-\;&&z&&\;=\;&&1&\\2x&&\;-\;&&2y&&\;+\;&&4z&&\;=\;&&-2&\\-x&&\;+\;&&{\tfrac {1}{2}}y&&\;-\;&&z&&\;=\;&&0&\end{alignedat}}

is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by

{\displaystyle {\begin{alignedat}{2}x&\,=\,&1\\y&\,=\,&-2\\z&\,=\,&-2\end{alignedat}}} {\begin{alignedat}{2}x&\,=\,&1\\y&\,=\,&-2\\z&\,=\,&-2\end{alignedat}}

since it makes all three equations valid. The word "system" indicates that the equations are to be considered collectively, rather than individually.