Final answer:
To solve the system of equations using the elimination method, first, multiply the first equation by 10 and the second equation by 3. Then subtract the second equation from the first to eliminate y. Solve for x and substitute it back into one of the equations to find y. The solution is x = 7.857 and y = -8.095.
Step-by-step explanation:
To solve the system of equations, we can use the elimination method. Multiply the first equation by 10 to eliminate the decimals: 2x - 3y = 40. Next, multiply the second equation by 3 to make the coefficients of y equal: 6.9x - 3y = 1.5. Subtract the second equation from the first to eliminate y: (2x - 3y) - (6.9x - 3y) = 40 - 1.5. Simplify: -4.9x = 38.5. Divide both sides by -4.9 to solve for x: x = -38.5 / -4.9 = 7.857. Now substitute the value of x back into one of the original equations to solve for y. Using the first equation, we have 0.2(7.857) - 0.3y = 4. Simplify: 1.5714 - 0.3y = 4. Rearrange the equation to solve for y: -0.3y = 4 - 1.5714, -0.3y = 2.4286, y = 2.4286 / -0.3 = -8.095.
The solution to the system of equations is x = 7.857 and y = -8.095.