Determine the number of solutions for the following system of equations
2x+5y=7
10y=-4x+14
1)Exactly one solution
2)No solutions
3)infinite solutions
4)Exactly 2 solutions
I solved the equations and got
y=7-2X/5
y=-4X+14/10
and I said infinite solutions. Is that correct?
4 x + 10 y = 14 is the first equation times 2
4 x + 10 y = 14 is the second equation
there is a y for any real x, in other words an infinite number of solutions since both equations are for the same line
so what I had is correct.
Thank you for checking and explaining the work!!
You only rearranged them.
You solved for y in terms of x
no
To determine the number of solutions for the given system of equations, you need to compare the slopes and intercepts of the two equations.
The given system of equations is:
1) 2x + 5y = 7
2) 10y = -4x + 14
First, let's rewrite the second equation in the standard form:
2x + 5y = 7 [Equation 1]
4x + 10y = 14 [Equation 2]
Now, we can compare the slopes and intercepts:
Slope (m1) of Equation 1 = -2/5
Slope (m2) of Equation 2 = -4/10 = -2/5
The slopes are the same (-2/5), which means that the lines are parallel or coincident.
To determine the number of solutions, we need to compare the intercepts:
Intercept (b1) of Equation 1 = 7
Intercept (b2) of Equation 2 = 14
Since the y-intercepts are different (7 ≠ 14), the lines are parallel and do not intersect, which implies no solution.
Therefore, the correct answer is 2) No solutions.