kase12
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99 points!! Help ASAP
Solve the system of equations using the Linear Combination Method.
5. 4x-9y=1
-4x+6y=-2

6. 3x-2y=14
2x+2y=6

Respuesta :

hermentotiph
· PROBLEM 5:

[tex]\begin{cases}&4x-9y=1\\&-4x+6y=-2\end{cases}[/tex]

[tex]\underline{\textbf{Combination\ method:}}\\ \\.\qquad\not{4x}-9y=1\\.\quad\ -\not{4x}+6y=-2\\ ============\\.\qquad\quad\ -3y=-1\\ \\.\qquad\qquad\ \ y= \dfrac{-1}{-3}\\ \\ \\.\quad\qquad\qquad\ y= \dfrac{1}{3}\quad\checkmark\\ \\ \\\textbf{Add\ "y"\ in\ Eq.\ 1:}\\ \\4x-9\left( \dfrac{1}{3}\right)=1\\ \\ \\4x-\not{9}\left( \dfrac{1}{\not{3}}\right)=1\\ \\4x-3(1)=1\\ \\4x-3=1\\ \\4x=1+3\\ \\4x=4\\ \\x= \dfrac{4}{4}\\ \\x=1\quad\checkmark[/tex]

[tex]\mathbb{ANSWER:}\Longrightarrow\boxed{\boxed{\boldsymbol{x=1\ ;\ y= \dfrac{1}{3} }}}[/tex]

· PROBLEM 6:

[tex]\begin{cases}&3x-2y=14\\&2x+2y=6\end{cases}[/tex]

[tex]\underline{\textbf{Combination\ method:}}\\ \\.\quad\quad\ 3x-\not{2y}=14\\.\quad\quad\ 2x+\not{2y}=6\\ ============\\.\quad\quad\ 5x=20\\ \\.\quad\ \quad\ x= \dfrac{20}{5}\\ \\.\quad\ \quad\ x=4\quad\checkmark\\ \\ \\\textbf{Add\ "x"\ in\ Eq.\ 2:}\\ \\2(4)+2y=6\\ \\8+2y=6\\ \\2y=6-8\\ \\2y=-2\\ \\y= \dfrac{-2}{2}\\ \\y=-1\quad\checkmark[/tex]

[tex]\mathbb{ANSWER:}\Longrightarrow\boxed{\boxed{\boldsymbol{x=4\ ;\ y=-1}}}\\ \\ \\\textbf{HOPE\ THIS\ HELPS...!!}[/tex]
Padoru

The Linear Combination method is where you add both equations into a single equation.

First question:

[tex]4x-9y=1[/tex]

[tex]-4x+6y=-2[/tex]

Add the equations together:

[tex](4x-4x)+(6y-9y)=(1-2)[/tex]

[tex]-3y=-1[/tex]

Divide both sides by -3

[tex]\boxed{y=-\dfrac{1}{3}}[/tex]

Plug this value into the first equation and solve for x

[tex]4x-9\Big(-\dfrac{1}{3}\Big)=1[/tex]

[tex]4x+3=1[/tex]

Subtract both sides by 3

[tex]4x=-2[/tex]

Divide both sides by 4

[tex]\boxed{x=-\dfrac{1}{2}}[/tex]

Second question:

[tex]3x-2y=14[/tex]

[tex]2x+2y=6[/tex]

Add both equations together:

[tex](3x+2x)+(2x-2y)=(14+6)[/tex]

[tex]5x=20[/tex]

Divide both dies by 5

[tex]\boxed{x=4}[/tex]

Plug this value into the second equation and solve for y

[tex]2(4)+2y=6[/tex]

[tex]8+2y=6[/tex]

Subtract both sides by 8

[tex]2y=-2[/tex]

Divide both sides by 2

[tex]\boxed{y=-1}[/tex]

Let me know if you need any clarifications, thanks!

~ Padoru

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