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Determine whenever this system of linear equations is consistent and independent , consistent and dependent , or inconsistent. Show your solution.


[tex]2x + y = - 6 \\ 2x + y = 10[/tex]
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Sagot :

HakuYukiidn

Answer:

Just look at the picture for solution.

Step-by-step explanation:

Consistent/Independent has one solution wherein two lines intersectes and forms a solution.

Consistent/Dependent has infinite solution since two lines coincide with each other.

Inconsistent has no solution since both lines are parallel and do not intersect.

View image HakuYuki
View image HakuYuki

[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

[tex]\underline{\mathbb{DIRECTION}:}[/tex]

  • Determine whenever this system of linear equations is consistent and independent , consistent and dependent , or inconsistent. Show your solution.

[tex]\qquad \qquad \begin{gathered}\begin{cases} \sf \: 2x + y = - 6\\ \sf \: 2x + y = 10\end{cases}\end{gathered} [/tex]

[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

[tex]\underline{\mathbb{SOLUTION}:}[/tex]

» Transforming these equations into the slope - intercept form.

[tex]\sf \green{Equation \: 1:2x + y = - 6 }\\ \: \: \: \: \: \: \: \: \: \: \: \sf \: 2x - 2x + y = - 6 - 2x \\ \sf \: y = - 2x - 6 \\ \: \: \boxed { \sf \red{ m = - 2 \: ;b=-6}} \\ \\ \sf \green{Equation \: 2:2x + y = 10 }\\ \: \: \: \: \: \: \: \: \: \: \: \sf \: 2x - 2x + y = 10 - 2x \\ \sf \: y = - 2x + 10 \\ \: \: \boxed { \sf \red{ m = - 2 \: ;b=10}}[/tex]

» In can be observed that slope of equation [tex]\bold \red{1}[/tex] is equal to the slope of equation [tex]\bold \red{2}[/tex] but the y-intercept of equation [tex]\bold \red{1}[/tex] is not equal to the y-intercept of equation [tex]\bold \red{2}[/tex]. We say that [tex]\bold\red {m_1 = m_2}[/tex] and [tex]\bold\red {b_1 ≠ b_2}[/tex].

[tex]\therefore[/tex] Therefore , this system of linear equation is Inconsistent because of having no solution.

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Learn More!

  • » System of Inconsistent equations - This is a system' of equations having no solution. The slopes of the lines defined by the equation are equal or have no slopes and the y-intercept are equal.

  • » System' of Consistent and dependent equations - This is a system of linear equations having infinitely many solution. The slopes of the lines defined by the equations are equal and the y-intercept are also equal.

  • » System' of Consistent and Independent equations - This is a system of linear equations having exactly one solution. The slopes of the line defined by the equation are not equal and the y-intercept are could be equal or unequal.

[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

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