Which is the solution to this pair of linear equations?
3x + y = 6
−x + 2y = 12
A (0, 12)
B (0, 6)
C (0, −6)
D (6, 0)

(0,6)

Step-by-step explanation:

So let's start with the top problem.

You have: 3x + y = 6

First, you need to move the number with the X to the right. You will need to subtract the 3x over to the 6

Ex:

3x + y = 6

-3 -3

This now gives you: y = -3x + 6

This is because: When you subtract the 3x, it cannot make the 6 a 3 because the 3 has an x along side it. Because of this, you have to make them separate. The 3x becomes a negative due to subtraction. When the 3x cannot go into anything, it will keep the minus with it and become negative. The y stays the same because it's not accompanying any number.

Now that your problem is in Slope Intercept Form, we can move onto the second problem

Here you have: -x + 2y = 12

First, just like last time, you have to move the -1x to the right. When a variable doesn't have a number next to it, it's always a 1.

For this one, you have to add the -x

Ex:

-x + 2y = 12

+x +x

This now gives you: 2y = x + 12

This is because The -x is now positive because you added it to the 12, but since the -1 is accompanying an x, it cannot go into the 12 and make it 13. It stays x. The 2y stays here as well.

For your second step, you have to take the 2 from the 2y and Divide it to ALL the numbers on the right side.

Ex:

2y = x + 12

÷2 ÷2 ÷2

This now gives you: y = 1/2x + 6

This is because: Since you have to convert the problem to slope intercept form, the y stays on the left, while the 2 divides all the numbers. Since the 2 cannot divide with the 1x since the 1 is accompanying an x, it becomes a fraction.

Now we have: y = -3x + 6

y = 1/2 + 6

What you do next: Personally, I do not have graphing paper on me, so I used Desmos Online Calculator and typed in both problems to get (0,6), but if you're graphing on normal graph paper, you just have to graph the problems like you did in System of Linear Equations.

If you have any more questions about anything, I'm always here to help :)

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )