How many solutions does the following system have?
{ 16x - 8y=20
{ 4x - 2y= 5
A. O
B. 1
C. 2
D. Infinitely many
m1 = -A/B = -16/-8 = 2
m2 = -4/-2 = 2
m1 = m2. So the lines do not intersect.
Therefore, there is no solution.
Correction: The Eqs are identical(divide
the 1st Eq by 4). So we have an infinite # of solutions.
To determine the number of solutions for the given system of equations, let's use a method called elimination.
First, let's rewrite the given system of equations:
Equation 1: 16x - 8y = 20
Equation 2: 4x - 2y = 5
We can eliminate one variable by manipulating one of the equations to have a coefficient of either -8 or 8 for the y-variable. To do this, multiply Equation 2 by -2:
Equation 1: 16x - 8y = 20
Equation 2: -8x + 4y = -10
Now, we can add the two equations together:
(16x - 8y) + (-8x + 4y) = 20 + (-10)
(16x - 8x) + (-8y + 4y) = 10
8x - 4y = 10
Now we have a new equation:
Equation 3: 8x - 4y = 10
If we compare Equation 3 to Equation 1, we can see that they represent the same line. This means that they have an infinite number of solutions.
Therefore, the answer is (D) Infinitely many solutions.