Answer:
<h2>B) one solution</h2>
Step-by-step 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 <u>has one solution</u>
