Solve each system by graphing to find the point of intersection of the two lines.

Let’s solve each system by graphing — that means we’ll find where the two lines cross (the point of intersection). We can do this by plotting both lines on the same grid and seeing where they meet. But since we’re doing it step-by-step without actual drawing, we’ll use algebra to find the exact point — which is what graphing would show us.

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Problem 1:
y = 2x - 3
y = -3x + 2

Since both equal y, set them equal to each other:

2x - 3 = -3x + 2

Add 3x to both sides:

5x - 3 = 2

Add 3 to both sides:

5x = 5

Divide by 5:

x = 1

Now plug x = 1 into either equation to find y. Let’s use the first one:

y = 2(1) - 3 = 2 - 3 = -1

So the point of intersection is (1, -1)

✔ Check with second equation: y = -3(1) + 2 = -3 + 2 = -1 → matches!

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Problem 2:
y = -(5/3)x + 1
y = -(1/3)x - 3

Set them equal:

-(5/3)x + 1 = -(1/3)x - 3

Multiply every term by 3 to eliminate denominators:

-5x + 3 = -x - 9

Add 5x to both sides:

3 = 4x - 9

Add 9 to both sides:

12 = 4x

Divide by 4:

x = 3

Now plug x = 3 into either equation. Use the second one (easier numbers):

y = -(1/3)(3) - 3 = -1 - 3 = -4

Point of intersection: (3, -4)

✔ Check with first equation: y = -(5/3)(3) + 1 = -5 + 1 = -4 → matches!

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Problem 3:
y = -x + 1
x = 3

This one is easy! The second equation says x is always 3. So plug x = 3 into the first equation:

y = -(3) + 1 = -2

Point of intersection: (3, -2)

✔ That’s it — vertical line at x=3 crosses the slanted line at y=-2.

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Problem 4:
y = 4x + 1
y = x - 2

Set them equal:

4x + 1 = x - 2

Subtract x from both sides:

3x + 1 = -2

Subtract 1:

3x = -3

Divide by 3:

x = -1

Plug into second equation (simpler):

y = (-1) - 2 = -3

Point of intersection: (-1, -3)

✔ Check with first: y = 4(-1) + 1 = -4 + 1 = -3 → matches!

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Final Answer:
1) (1, -1)
2) (3, -4)
3) (3, -2)
4) (-1, -3)