Solve the following system of equations using the elimination method.
0.1x +0.3y =0.9, 0.1x - 0.3y = 0.2
• (11/2,7/6)
• (-7/6,11/2)
• (11/2,-7/6)
• There is no solution
To solve the system of equations using the elimination method, we need to eliminate one variable by adding the two equations together.
Starting with the given system of equations:
0.1x + 0.3y = 0.9
0.1x - 0.3y = 0.2
Adding the two equations together, the y terms will cancel out:
(0.1x + 0.3y) + (0.1x - 0.3y) = 0.9 + 0.2
0.1x + 0.1x + 0.3y - 0.3y = 1.1
0.2x = 1.1
Dividing both sides of the equation by 0.2, we get:
x = 1.1 / 0.2
x = 11/2
Now substitute the value of x back into one of the original equations (either one will work) to solve for y:
0.1(11/2) + 0.3y = 0.9
11/20 + 0.3y = 0.9
Subtracting 11/20 from both sides of the equation:
0.3y = 0.9 - 11/20
0.3y = 36/40 - 11/20
0.3y = 25/40
Dividing both sides of the equation by 0.3, we get:
y = (25/40) / 0.3
y = 25/40 * 10/3
y = 250/120
y = 25/12
Therefore, the solution to the system of equations is (11/2, 25/12).
None of the given answer choices match this solution, indicating that there is no correct solution listed.