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What is the point of intersection of the lines y = 3x + 1 and y = -x + 5?
What is the point of intersection of the lines y = 3x + 1 and y = -x + 5?
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Practice Questions
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Q1
What is the point of intersection of the lines y = 3x + 1 and y = -x + 5?
(1, 4)
(2, 7)
(3, 10)
(4, 13)
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Setting 3x + 1 = -x + 5 gives 4x = 4, thus x = 1. Substituting x back gives y = 4. The intersection point is (1, 4).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the point of intersection of the lines y = 3x + 1 and y = -x + 5?
Solution:
Setting 3x + 1 = -x + 5 gives 4x = 4, thus x = 1. Substituting x back gives y = 4. The intersection point is (1, 4).
Steps: 9
Show Steps
Step 1: Write down the two equations of the lines: y = 3x + 1 and y = -x + 5.
Step 2: Since both equations equal y, set them equal to each other: 3x + 1 = -x + 5.
Step 3: To solve for x, first add x to both sides: 3x + x + 1 = 5.
Step 4: This simplifies to 4x + 1 = 5.
Step 5: Next, subtract 1 from both sides: 4x = 4.
Step 6: Now, divide both sides by 4 to find x: x = 1.
Step 7: Substitute x = 1 back into one of the original equations to find y. Using y = 3x + 1: y = 3(1) + 1.
Step 8: This simplifies to y = 3 + 1, so y = 4.
Step 9: The point of intersection of the two lines is (1, 4).
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