Question

Which of the following ordered pairs are solutions to the system of equations below?

a. (1, 6)
b. (1, -6)
3. (-1, -6)
4. (-1, 6)

Answer 1

Option 4.

For clear understanding refer to the attachment.

Answer 2

Given :-

• A system of linear equation in two variables .

To Find :-

• The solution set of the system .

Solution :-

The given system of equation is ,

`\begin{cases} 3x + 2y = 9\dots (i) \\\\ y = 4x + 10 \dots (ii)\end{cases}`

Firstly , taking equation (ii) ,

`y = 4x +10`

On subtracting y on both sides, we have ;

`4x - y +10 = 0`

Multiplying both sides by 2 ,

`2(4x -y+10)=2(0)`

Simplify,

`8x - 2y = -20 \dots (iii)`

Adding equation (i) and (iii) ,

`3x + 2y + 8x - 2y = -20+9`

Add and subtract the like terms ,

`11x = -11`

Divide both sides by 11 ,

`x = -1`

Now substitute this value in equation (i) ,

`3(-1) + 2y = 9\\ \\ -3 + 2y = 9 \\\\ 2y = 9+3 \\\\ 2y = 12 \\\\ y =(12)/(2)\\\\ y = 6`

Hence the correct option is 4 (-1,6) .

I hope this helps . Let me know if you need any further clarification .