Answer
There is one solution: (2, 1), or x = 2, y = 1.
Work Step by Step
Equation 1: 0.05x - 0.03y = 0.07
Equation 2: 0.07x + 0.02y = 0.16
Let's start by solving for the x variable. To eliminate variable y, we can get both y values to be their lowest common multiple, which is 0.06 for the numbers 0.02 and 0.03.
1: 2(0.05x - 0.03y) = 2(0.07)
0.1x - 0.06y = 0.14 (distributive property)
2: 3(0.07x + 0.02y) = 3(0.16)
0.21x + 0.06y = 0.48
Our new 2 equations contain a +0.06y and -0.06y. We can add the equations to eliminate this variable.
Equation 1: 0.1x - 0.06y = 0.14
Equation 2: + 0.21x + 0.06y = 0.48
= .31x + 0y = 0.62
We can eliminate the 0y because it cancels out. This leaves us with 0.31x = 0.62, and dividing both sides by 0.31 gets x = 2 (.62 / .31= 2).
To solve for y, plug the x value (2) into either of the original equations.
0.05(2) - 0.03y = 0.07 (plug in)
0.1 - 0.03y = 0.07 (simplify)
-0.03y = -0.03 (subtract 0.1 from both sides)
y = 1 (divide each side by -0.03)
