Question

How many solutions are there to the system of equations? {-4x - 5y = 5 -0.08x + 0.10y = 0.10} A) no solutions B)one solution C)two solutions D)an infinite number of solutions

Answer 1

B) one solution

Explanation:

Given the system of equations -4x - 5y = 5 and -0.08x + 0.10y = 0.10, to know the number of solutions the system of equation has, we need to solve for the values of x and y if possible.

-4x - 5y = 5... 1

-0.08x + 0.10y = 0.10... 2

Multiplying equation 2 by 100 will give -8x+10y = 10

The resulting system of equation will be;

-4x - 5y = 5 ...3 * 8

-8x + 10y = 10... 4 * 4

Using the elimination method to solve the equation, multiplying eqn 3 by 8 and eqn 4 by 4 we have;

-32x-40y = 40

-32x+40y = 40

Subtracting both resulting equations to eliminate x will give;

-40y-40y = 0

-80y = 0

y = 0

Substituting y = 0 into equation 3 to get x we have;

-4x-5(0) = 5

-4x = 5

x = -5/4

The solution to the system of equations is (0, -5/4). This shows that the system of equations only has one solution