Question

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

Answer 1

· PROBLEM 5:


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


`\underline{\textbf{Combination\ method:}}\\ \\.\qquad\\ot{4x}-9y=1\\.\quad\ -\\ot{4x}+6y=-2\\ ============\\.\qquad\quad\ -3y=-1\\ \\.\qquad\qquad\ \ y= (-1)/(-3)\\ \\ \\.\quad\qquad\qquad\ y= (1)/(3)\quad\checkmark\\ \\ \\\textbf{Add\`


`\mathbb{ANSWER:}\Longrightarrow\boxed{\boxed{\boldsymbol{x=1\ ;\ y= (1)/(3) }}}`

· PROBLEM 6:


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


`\underline{\textbf{Combination\ method:}}\\ \\.\quad\quad\ 3x-\\ot{2y}=14\\.\quad\quad\ 2x+\\ot{2y}=6\\ ============\\.\quad\quad\ 5x=20\\ \\.\quad\ \quad\ x= (20)/(5)\\ \\.\quad\ \quad\ x=4\quad\checkmark\\ \\ \\\textbf{Add\`


`\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=-(1)/(3)}`

Plug this value into the first equation and solve for x

`4x-9\Big(-(1)/(3)\Big)=1`

`4x+3=1`

Subtract both sides by 3

`4x=-2`

Divide both sides by 4

`\boxed{x=-(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