How many solutions does then system of equation have?
y-5x = -6 and 3y-15x=-12
So 8 years later and nobody has given an actual answer ok great
none
those two lines have the same slope of 5
so they are parallel but they do not have the same y axis intercept so they never touch each other in two dimensional space.
None
Well, let's see. If we put on our detective hats and investigate these equations, we might find something fishy going on. It seems like both equations can be simplified by a factor of 3. This leads us to conclude that these equations are actually the same equation in disguise!
In other words, these two lines are so close, they're practically holding hands and singing kumbaya. So, we have ourselves an infinite number of solutions! It's like a party where everyone gets an answer. How delightful!
To determine the number of solutions for a system of equations, we can use the concept of parallel lines and intersecting lines.
Let's rearrange the equations:
Equation 1: y - 5x = -6
Equation 2: 3y - 15x = -12
Now, let's determine the slopes of the lines represented by each equation:
The equation of a line in slope-intercept form is y = mx + b, where m represents the slope of the line.
In Equation 1, y - 5x = -6, we can rewrite it as y = 5x - 6. The slope of this line is 5.
In Equation 2, 3y - 15x = -12, we can rewrite it as y = 5x - 4. The slope of this line is also 5.
Since both equations have the same slope, the lines they represent are parallel. Parallel lines never intersect, meaning the system of equations has no solution.
Therefore, the system of equations has no solution.