# Algebra

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How many solutions does this system of equations have?

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

One, two, infinitely many, or no solutions? My answer is no solutions.

• Algebra -

y = 4 x + 3
y = 4 x + 3/2

two lines with the same slope but different y axis intercepts. They never cross each other and therefore there is no solution to this problem.

• Algebra -

Thanks. I have a couple more:

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

Answer: Infinitely many solutions

x - 3y = 15 and 3x - 9y = 4

Answer: Infinitely many solutions

y - 5x = -6 and 3y - 15x = -12

Answer: One solution

• Algebra -

x - 3y = 15 and 3x - 9y = 4
x - 3 y = 4/3
Same slope, never cross NO solutions !

Answer: Infinitely many solutions DIASAGREE

y - 5x = -6 and 3y - 15x = -12
y - 5 x = -4
AGAIN, they are NOT the same. They are PARALLEL and never cross NO solutions
same m = slope = either the same (infinite solutions of parallel (different y intercept) which means ZERO solutions

Answer: One solution NO!

• Algebra -

Seems like both have no solutions. I went a bit off in my calculation. I see now.

• Algebra -

When in doubt, sketch a graph

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