Where do the lines 2x + 3y = 8 and y = 3x + 16 intersect?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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At the point of intersectio of two lines the x and y-coordinates are equal. The point of intersection of the lines 2x + 3y = 8 and y = 3x + 16 can be determined by solving them for x and y.

2x + 3y = 8...(1)

y = 3x + 16...(2)

Substitute y = 3x + 16 in (1)

2x + 3(3x + 16) = 8

=> 2x + 9x + 48 = 8

=> 11x = -40

=> x = `-40/11`

y = `3(-40/11) + 16`

=> `-120/11 + 16`

=>` 56/11`

The point of intersection of the lines 2x + 3y = 8 and y = 3x + 16 is `(-40/11, 56/11)`

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