Question

solving linear equation (3x+5)/7 + (4x-9)/6 = 38x and check the solution.

Answer 1

The system of equations are and its solution is .

Substitute the values of in the above linear system.

Equation 1: .

Equation 2: .

Neither variable has a common coefficient.The coefficient  of the a - variables are 2 and 1 and their least common multiple is 2, so multiply each equation by the value  that will make the a - coefficient 2.

To get two equations that contain opposite terms multiply the second equation by 2.

 

Write the equations in column form and add the corresponding columns to eliminate a - variable.

Answer 2

The linear equation is .

Fractions with different denominators can not be added. So, write the equation with common denominator.

Find the least common denominator L.C.M.

Multiples of 7 = 7, 14, 21, 28, 35, 42, ......

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, .........

Least Common Multiple of 7 and 6 is 42

Write the left hand side equation with common denominator.

Since denominators are same add the numerators over the denominator.

Multiply each side by 42.

Cancel common terms.

Apply distributive properties : .

Subtract 1596x from each side.

Apply Additive Inverse Property: a + (-a) = 0.

Group like terms.

Combine like terms.

Divide each side by negative 1550.

Cancel common terms.

.

The solution is .

Answer 3

Contd....

Check :

Substitute the value of in given linear equation.

.

The above statement is true.

So, is the solution of .