Slope-Intercept Form
y = 2x + 5
y = -x + 7
Set 2x + 5 = -x + 7. Combine like terms: 3x = 2. Solve for x: x = 1.
Substitute x = 1 into y = 2x + 5: y = 2(1) + 5 = 7.
Answer: (1, 7).
y = 2x + 5
x + y = 7
Substitute y = 2x + 5 into x + y = 7:
x + (2x + 5) = 7. Combine like terms: 3x + 5 = 7. Solve for x: 3x = 2, so x = 2.
Substitute x = 2 into y = 2x + 5: y = 2(2) + 5 = 9.
Answer: (2, 9).
(2, 1)
y = 3x - 4
y = -2x + 6
Set 3x - 4 = -2x + 6. Combine like terms: 5x = 10. Solve for x: x = 2.
Substitute x = 2 into y = 3x - 4: y = 3(2) - 4 = 2.
Answer: (2, 2).
y = -x + 4
2x - y = -6
Substitute y = -x + 4 into 2x - y = -6:
2x - (-x + 4) = -6. Simplify: 2x + x - 4 = -6. Combine like terms: 3x - 4 = -6. Solve for x: 3x = -2, so x = -1.
Substitute x = -1 into y = -x + 4: y = -(-1) + 4 = 5.
Answer: (-1, 5).
(2, 2)
y = x + 9
y = -3x + 3
Set x + 9 = -3x + 3. Combine like terms: 4x = -6. Solve for x: x = -2.
Substitute x = -2 into y = x + 9: y = -2 + 9 = 7.
Answer: (-2, 7).
y = 3x - 1
x - y = 3
Substitute y = 3x - 1 into x - y = 3:
x - (3x - 1) = 3. Simplify: x - 3x + 1 = 3. Combine like terms: -2x + 1 = 3. Solve for x: -2x = 2, so x = -1.
Substitute x = -1 into y = 3x - 1: y = 3(-1) - 1 = -4.
Answer: (-1, -4).
(3, 1)
y = -x + 8
y = 4x - 2
Set -x + 8 = 4x - 2. Combine like terms: 5x = 10. Solve for x: x = 2.
Substitute x = 2 into y = -x + 8: y = -2 + 8 = 6.
Answer: (2, 6).
y = -2x + 7
3x + y = 10
Substitute y = -2x + 7 into 3x + y = 10:
3x + (-2x + 7) = 10. Simplify: 3x - 2x + 7 = 10. Combine like terms: x + 7 = 10. Solve for x: x = 3.
Substitute x = 3 into y = -2x + 7: y = -2(3) + 7 = 1.
Answer: (3, 1).
(3, -2)
y = 5x - 10
y = -x + 12
Set 5x - 10 = -x + 12. Combine like terms: 6x = 22. Solve for x: x = 3.
Substitute x = 3 into y = 5x - 10: y = 5(3) - 10 = 5.
Answer: (3, 5).
y = 4x - 3
x + 2y = 7
Substitute y = 4x - 3 into x + 2y = 7:
x + 2(4x - 3) = 7. Simplify: x + 8x - 6 = 7. Combine like terms: 9x - 6 = 7. Solve for x: 9x = 13, so x = 1.
Substitute x = 1 into y = 4x - 3: y = 4(1) - 3 = 1.
Answer: (1, 1).
(2, 1)