Math worksheet featuring four problems where students solve systems of linear equations by plotting lines on a coordinate plane.

Let’s solve each system of linear equations by graphing. Since we’re solving by graphing, we’ll find where the two lines intersect — that point (x, y) is the solution.

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Problem 1:

Equations:
- \( y = -\frac{4}{5}x + 5 \)
- \( y = 1 \)

The second equation is a horizontal line at y = 1.

To find the intersection, plug y = 1 into the first equation:

\( 1 = -\frac{4}{5}x + 5 \)

Subtract 5 from both sides:

\( 1 - 5 = -\frac{4}{5}x \)

→ \( -4 = -\frac{4}{5}x \)

Multiply both sides by 5 to eliminate denominator:

→ \( -20 = -4x \)

Divide both sides by -4:

→ \( x = 5 \)

So the solution is (5, 1)

✔ Check: Plug x=5 into first equation → y = -4/5 * 5 + 5 = -4 + 5 = 1 ✔️
Second equation: y=1 ✔️

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Problem 2:

Equations:
- \( y = \frac{1}{4}x + 2 \)
- \( y = x - 1 \)

Set them equal since both equal y:

\( \frac{1}{4}x + 2 = x - 1 \)

Subtract \( \frac{1}{4}x \) from both sides:

→ \( 2 = \frac{3}{4}x - 1 \)

Add 1 to both sides:

→ \( 3 = \frac{3}{4}x \)

Multiply both sides by 4:

→ \( 12 = 3x \)

Divide by 3:

→ \( x = 4 \)

Now plug x=4 into either equation to get y. Use second one: y = 4 - 1 = 3

Solution: (4, 3)

✔ Check in first equation: y = (1/4)(4) + 2 = 1 + 2 = 3 ✔️

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Problem 3:

Equations:
- \( y = -\frac{8}{3}x + 3 \)
- \( y = -\frac{4}{3}x - 1 \)

Set equal:

\( -\frac{8}{3}x + 3 = -\frac{4}{3}x - 1 \)

Add \( \frac{8}{3}x \) to both sides:

→ \( 3 = \frac{4}{3}x - 1 \)

Add 1 to both sides:

→ \( 4 = \frac{4}{3}x \)

Multiply both sides by 3:

→ \( 12 = 4x \)

Divide by 4:

→ \( x = 3 \)

Plug x=3 into second equation: y = -4/3 * 3 - 1 = -4 - 1 = -5

Solution: (3, -5)

✔ Check in first equation: y = -8/3 * 3 + 3 = -8 + 3 = -5 ✔️

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Problem 4:

Equations:
- \( y = -3 \)
- \( y = \frac{1}{4}x - 2 \)

First equation is horizontal line at y = -3.

Plug y = -3 into second equation:

→ \( -3 = \frac{1}{4}x - 2 \)

Add 2 to both sides:

→ \( -1 = \frac{1}{4}x \)

Multiply both sides by 4:

→ \( x = -4 \)

Solution: (-4, -3)

✔ Check: Plug x=-4 into second equation → y = (1/4)(-4) - 2 = -1 - 2 = -3 ✔️
First equation: y=-3 ✔️

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Final Answer:

1. (5, 1)
2. (4, 3)
3. (3, -5)
4. (-4, -3)