Linear equations with fractions can be solved in the same way as linear equations with whole number. Instead of the coefficients of the terms that have to be worked being whole numbers they are fractions. Else, the fractions can be eliminated by multiplying the terms with appropriate numbers.
For instance, take the set of equations
(3/2)x + (4/5)y = (1/2) and (2/3)x + (1/2)y = 2/3
The equation (3/2)x + (4/5)y = (1/2) is equivalent to 15x + 8y = 5 and the equation (2/3)x + (1/2)y = 2/3 is equivalent to 4x + 3y = 4
Solving linear equation with fractions means to find the value for the unknown variable in the linear equation. Further when we put that value of the variable in the equation, it satisfies the equation and the value of the left side of the equation is equal to the right side of the equation.