Worksheet for solving systems of linear equations using graphing method.

Let’s solve the two systems of equations by graphing, as instructed.

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First System (left side):

Equations:
1. y = 3x + 1
2. y = x + 5

We need to graph both lines and find where they intersect — that point is the solution.

Step 1: Graph y = 3x + 1

- This is in slope-intercept form (y = mx + b), so:
- Slope (m) = 3 → rise 3, run 1
- y-intercept (b) = 1 → start at (0, 1)

Plot point (0, 1). From there, go up 3, right 1 → (1, 4). Draw line through these points.

Step 2: Graph y = x + 5

- Slope = 1 → rise 1, run 1
- y-intercept = 5 → start at (0, 5)

Plot (0, 5). Go up 1, right 1 → (1, 6). Draw line.

Step 3: Find intersection

Look for where the two lines cross.

Try plugging in x-values to see if y-values match:

Try x = 2:
- First equation: y = 3(2) + 1 = 7
- Second equation: y = 2 + 5 = 7 → Match!

So the lines intersect at (2, 7).

✔ Solution for first system: (2, 7)

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Second System (right side):

Equations:
1. y = x + 2
2. y = -x + 4

Again, graph both and find intersection.

Step 1: Graph y = x + 2

- Slope = 1, y-intercept = 2 → start at (0, 2)
- Next point: (1, 3)

Draw line.

Step 2: Graph y = -x + 4

- Slope = -1 → down 1, right 1
- y-intercept = 4 → start at (0, 4)
- Next point: (1, 3)

Wait — both lines pass through (1, 3)? Let’s check:

For y = x + 2: when x=1, y=3 → yes
For y = -x + 4: when x=1, y=3 → yes

So they intersect at (1, 3).

✔ Solution for second system: (1, 3)

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Final Answer:
First system solution: (2, 7)
Second system solution: (1, 3)