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.

14 answers

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.

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

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!

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

When in doubt, sketch a graph

thats so dead Damon

Y=4x+3
Y=-x-2

Y=3x-2
Y=2(x-1)

Y=6x-10
Y=2(3x-5)

Y=-2x+2
Y=2x-2

3 (x+2y)=8

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

ummmm wth