FREE Solving Systems of Linear Equations digital version - Free Printable

Let’s solve each system of linear equations and match them to the correct ordered pair (x, y).

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System 1:

2x + y = 7
3x - y = 3

Add the two equations to eliminate y:

→ (2x + y) + (3x - y) = 7 + 3
→ 5x = 10
→ x = 2

Substitute x = 2 into first equation:

→ 2(2) + y = 7 → 4 + y = 7 → y = 3

✔ Solution: (2, 3)

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System 2:

x - y = 4
x + y = 2

Add the two equations:

→ (x - y) + (x + y) = 4 + 2
→ 2x = 6 → x = 3

Substitute x = 3 into second equation:

→ 3 + y = 2 → y = -1

✔ Solution: (3, -1)

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System 3:

2x + 3y = 8
3x + y = 5

Solve second equation for y:
→ y = 5 - 3x

Substitute into first equation:

→ 2x + 3(5 - 3x) = 8
→ 2x + 15 - 9x = 8
→ -7x = -7 → x = 1

Then y = 5 - 3(1) = 2

✔ Solution: (1, 2)

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System 4:

2x - 3y = 8
2x + 3y = 4

Add the two equations:

→ (2x - 3y) + (2x + 3y) = 8 + 4
→ 4x = 12 → x = 3

Substitute x = 3 into second equation:

→ 2(3) + 3y = 4 → 6 + 3y = 4 → 3y = -2 → y = -2/3

✔ Solution: (3, -2/3)

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System 5:

5x + y = 15
3x + 2y = 9

Solve first equation for y:
→ y = 15 - 5x

Substitute into second equation:

→ 3x + 2(15 - 5x) = 9
→ 3x + 30 - 10x = 9
→ -7x = -21 → x = 3

Then y = 15 - 5(3) = 0

✔ Solution: (3, 0)

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System 6:

-x + 2y = 10
x - 3y = -13

Add the two equations:

→ (-x + 2y) + (x - 3y) = 10 + (-13)
→ -y = -3 → y = 3

Substitute y = 3 into first equation:

→ -x + 2(3) = 10 → -x + 6 = 10 → -x = 4 → x = -4

✔ Solution: (-4, 3)

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System 7:

2x - 3y = 0
-2x + 2y = -2

Add the two equations:

→ (2x - 3y) + (-2x + 2y) = 0 + (-2)
→ -y = -2 → y = 2

Substitute y = 2 into first equation:

→ 2x - 3(2) = 0 → 2x - 6 = 0 → 2x = 6 → x = 3

✔ Solution: (3, 2)

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System 8:

y = 3x + 6
2y = -3x + 3

Substitute first equation into second:

→ 2(3x + 6) = -3x + 3
→ 6x + 12 = -3x + 3
→ 9x = -9 → x = -1

Then y = 3(-1) + 6 = -3 + 6 = 3

✔ Solution: (-1, 3)

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## ✔ Final Matching:

| System | Ordered Pair |
|--------|--------------|
| 2x + y = 7<br>3x - y = 3 | (2, 3) |
| x - y = 4<br>x + y = 2 | (3, -1) |
| 2x + 3y = 8<br>3x + y = 5 | (1, 2) |
| 2x - 3y = 8<br>2x + 3y = 4 | (3, -2/3) |
| 5x + y = 15<br>3x + 2y = 9 | (3, 0) |
| -x + 2y = 10<br>x - 3y = -13 | (-4, 3) |
| 2x - 3y = 0<br>-2x + 2y = -2 | (3, 2) |
| y = 3x + 6<br>2y = -3x + 3 | (-1, 3) |

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