3х-у=10 х/3+у+1/5=1

To solve the system of equations, we can use the method of substitution. Here's the step-by-step solution:

1. Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x: x/3 + y + 1/5 = 1 Subtract y and 1/5 from both sides: x/3 = 1 - y - 1/5 x/3 = 1 - (5y + 1)/5 Multiply both sides by 3 to isolate x: x = 3 - 3(5y + 1)/5 x = 3 - (15y + 3)/5 Simplify the expression: x = (15 - 15y - 3)/5 x = (12 - 15y)/5

2. Substitute the expression for x into the other equation. Substituting (12 - 15y)/5 for x in the first equation: 3(12 - 15y)/5 - y = 10 Multiply 3/5 through the parentheses: (36 - 45y)/5 - y = 10 Multiply through by 5 to get rid of the denominator: 36 - 45y - 5y = 50 Combine like terms: -50y + 36 = 50 Subtract 36 from both sides: -50y = 50 - 36 -50y = 14 Divide both sides by -50: y = 14/-50 y = -7/25

3. Substitute the value of y back into one of the equations to solve for x. Substituting -7/25 for y in the first equation: 3x - (-7/25) = 10 3x + 7/25 = 10 Subtract 7/25 from both sides: 3x = 10 - 7/25 3x = (250 - 7)/25 3x = 243/25 Divide both sides by 3 to isolate x: x = (243/25) / 3 Simplify: x = 243/75 x = 27/5

Therefore, the solution to the system of equations is x = 27/5 and y = -7/25.