For the following exercises, solve each system by any method.

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Expert Solution

Substitution method is one of the easiest algebraic methods of solving system of equations in two variables. It is based upon the concept of obtaining the solution using linear equations in one variable.

Consider the following system of linear equations in two variables:

3x + 6y = 11 …… (1)

2x + 4y = 9 …… (2)

Rewrite both equations in slope intercept form as:

3x + 6y = 11

6y = -3x + 11

y = - 3/6x + 11/6

y = -1/2x + 11/6 …… (3)

And

2x + 4y = 9

4y = -2/4x + 9/4

y = -1/2x + 9/4

y = -1/2x + 9/4 …… (4)

Observe that both the equations (3) and (4) have same slope and different y-intercepts.

Thus the lines are parallel.

Hence, the system of linear equations 3x + 6y = 11 and 2x + 4y = 9 have no solution.

Nabeel answered 1 year ago

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