solve 2x+3y=1 and 6y=-4x+2

Question

please help me solve this.

Answer 1

The equations are

2x  + 3y = 1   ---------> (1)

6y  = -4x + 2  ---------> (2)

Divide each side by 2 to (2).

3y  = - 2x + 1

Add 2x to each side.

2x + 3y  = 1   ---------> (3)

Observe the equations (1) & (3),these lines are equal lines.

So there is no solution.

Answer 2

Substitute Method:

The equations of linear system are .

Solve the equation 1 or 2 for x or y, since the x and y do not have a coefficient of .

Solve the equation 2: for y.

Divide each side by 6.

Substitute the value of  in the equation 1: and solve for x.

The above statement is true, so the system has number of infinity solutions.

Let , where a is any real number and .

The solution set .