Question

99 points!! Help ASAP

Answer 1

· PROBLEM 5:

$\begin{cases}&4x-9y=1\\&-4x+6y=-2\end{cases}$

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

$\mathbb{ANSWER:}\Longrightarrow\boxed{\boxed{\boldsymbol{x=1\ ;\ y= \dfrac{1}{3} }}}$

· PROBLEM 6:

$\begin{cases}&3x-2y=14\\&2x+2y=6\end{cases}$

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

$\mathbb{ANSWER:}\Longrightarrow\boxed{\boxed{\boldsymbol{x=4\ ;\ y=-1}}}\\ \\ \\\textbf{HOPE\ THIS\ HELPS...!!}$

Answer 2

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

First question:

$4x-9y=1$

$-4x+6y=-2$

Add the equations together:

$(4x-4x)+(6y-9y)=(1-2)$

$-3y=-1$

Divide both sides by -3

$\boxed{y=-\dfrac{1}{3}}$

Plug this value into the first equation and solve for x

$4x-9\Big(-\dfrac{1}{3}\Big)=1$

$4x+3=1$

Subtract both sides by 3

$4x=-2$

Divide both sides by 4

$\boxed{x=-\dfrac{1}{2}}$

Second question:

$3x-2y=14$

$2x+2y=6$

Add both equations together:

$(3x+2x)+(2x-2y)=(14+6)$

$5x=20$

Divide both dies by 5

$\boxed{x=4}$

Plug this value into the second equation and solve for y

$2(4)+2y=6$

$8+2y=6$

Subtract both sides by 8

$2y=-2$

Divide both sides by 2

$\boxed{y=-1}$

Let me know if you need any clarifications, thanks!

~ Padoru