Question

What point is the intersection of the graphs of the lines 2x - y = 3 and x+y = 3?

Answer 1

Answer:  (2, 1)

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Explanation:

Let's add the equations straight down

• The x terms add up to 2x+x = 3x
• The y terms add to -y+y = 0y = 0, so the y terms go away
• The right hand sides add to 3+3 = 6

After those three things happen, we're left with 3x = 6 which solves to x = 2 after dividing both sides by 3.

Now let's use this x value to find y

2x-y = 3

2(2)-y = 3

4-y = 3

-y = 3-4

-y = -1

y = 1

Or we could use the other equation

x+y = 3

2+y = 3

y = 3-2

y = 1

which gets us there in fewer steps.

So that's how we get to the final answer of (x,y) = (2,1)

The graph is shown below.