How many solutions does the system of equations below have? y=3x+4 y=3x+2 A) Only 1 solution B) Infinitely many solutions C) No solutions
the slopes are the same, so they are either
(a) parallel
(b) the same line
So, what do you think? What if x=0? Is 4=2?
Can you think of any value for x where 3x+4 = 3x+2 ?
How many solutions does the system of equations below have?
y
=
3
4
x
−
8
3
y
=
3
4
x
+
10
9
To determine the number of solutions, we need to examine the slopes of the two equations. Both equations have a slope of 3. Since the slopes are the same, the lines are parallel and will never intersect. Therefore, the system of equations has no solutions. The answer is C) No solutions.
To find the number of solutions for a system of equations, we need to compare their slopes and y-intercepts. The given system of equations is:
y = 3x + 4 ----(Equation 1)
y = 3x + 2 ----(Equation 2)
By comparing the slopes of both equations, which are 3 in this case, we can conclude that the lines represented by these equations are parallel.
When two lines are parallel, they never intersect, which means they have no common point of intersection. Therefore, the system of equations has no solutions.
Hence, the answer is C) No solutions.