Given two lines y=2x+1 and 3x − y =5 find the intersection poin of the two line

Mathematics

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Answer

(6, 13)
Graph of y = 2x + 1

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Key points of y = 2x + 1
Pointxy
x-intercept−0.50
y-intercept01

Step-by-step solution

3 steps

  1. Substitute the expression for yy from the first equation into the second equation.

    Given:

    1. y=2x+1y = 2x + 1
    2. 3x−y=53x - y = 5

    Substitute (1) into (2):

    3x−(2x+1)=53x - (2x + 1) = 5

  2. Solve for xx.

    3x−2x−1=53x - 2x - 1 = 5 x−1=5x - 1 = 5 x=5+1x = 5 + 1 x=6x = 6

  3. Substitute the value of xx back into the first equation to find yy.

    y=2(6)+1y = 2(6) + 1 y=12+1y = 12 + 1 y=13y = 13

    The intersection point is (6,13)(6, 13).

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