Final answer:
The given system of equations can be solved using the method of substitution. After isolating y in the first equation, substitute the expression for y in the second equation and solve for x. Finally, substitute the value of x back into one of the original equations to solve for y. The solution is x = 6.65 and y = -3.89.
Step-by-step explanation:
These two equations can be solved using the method of substitution. Step 1: Solve one equation for one variable. From the first equation, we can isolate y as follows: 7y = 6x + 8, y = (6x + 8)/7. Step 2: Substitute the expression for y in the second equation. Replace y in the second equation with (6x + 8)/7: 10x - 3((6x + 8)/7) = 46. Step 3: Simplify and solve for x. Multiply every term in the equation by 7 to eliminate the fraction: 70x - 18x - 24 = 322. Combine like terms: 52x = 346. Divide both sides of the equation by 52: x = 6.65.
Step 4: Substitute the value of x back into one of the original equations and solve for y. Using the first equation: 5(6.65) + 7y = 6. Simplify: 33.25 + 7y = 6. Subtract 33.25 from both sides: 7y = -27.25. Divide both sides by 7: y = -3.89.
So, the solution to the system of equations is x = 6.65 and y = -3.89.