Question

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

Answer 1

The intersection point of the lines 2x - y = 3 and x+y = 3 is (2, 1).

Step-by-step explanation:

To find the intersection point of the lines, we need to solve the system of equations formed by the two lines:

Equation 1: 2x - y = 3

Equation 2: x + y = 3

We can solve this system by either substitution or elimination method. Let's use the elimination method:

1. Add the two equations to eliminate the y variable: (2x - y) + (x + y) = 3 + 3
2. Simplify: 3x = 6
3. Divide by 3 to solve for x: x = 2
4. Substitute the value of x into either equation to solve for y:

• Using Equation 1: 2(2) - y = 3
• Simplify: 4 - y = 3
• Subtract 4 from both sides: -y = -1
• Multiply by -1 to solve for y: y = 1

Therefore, the intersection point of the two lines is (2, 1).

Answer 2

Answer: (2, 1)

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Step-by-step 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.