Question

Tell which equation you would choose to solve for one of the variables when solving the system by substitution. Then solve the system by substitution.

2x−3y=112x−3y=11     Equation 1

    x+2y=−5x+2y=−5      Equation 2

Answer 1

Substitution method is an algebraic method which is used to find the solution of a system of equations, In this method we find the value of one variable in the term of second variable with help of one equation,

Then substitute this vale in another equation

Now, Here the given system of equations,

2x − 3y = 11 -------(1)

x + 2y = −5 --------(2)

When we see the equations we find that it is easy to find the value of x with help the equation 2, ( Because here the coefficient of x is 1)

Thus, choosing equation 2 is the good idea,

From equation (2),

x = -5 - 2y --- (3)

By substituting this value in equation (1),

We get, 2(-5 - 2y) -3y = 11

-10 - 4y - 3y = 11

-10 - 7y = 11

-7y = 21

y = -3

By equation (3),

x = - 5 - 2 × - 3

x = - 5 + 6

x = 1

Thus, the solution of the given system is x = 1 and y = -3