Question

Fina wants to use substitution to solve the system of equations. Explain what she needs to do first before using substitution. Then solve the systems of equations

Answer 1

Explanation:

Step 1:

She Should Solve one of the equations for either x = or y = .(x and y are the variables)

Step 2:

Then Substitute the solution from step 1 into the other equation.

Step 3:

Then Solve this new equation.

Step 4:

Then Solve for the second variable.

Example 1: Solve the following system by substitution

3x+2y=6

x+y=6

Solution of example:

Step 1: Solve one of the equations for either x = or y = . We will solve second equation for y.

x+y=6

y=6−x

Step 2: Substitute the solution from step 1 into the second equation.

3x+2y=6

3x+2(6−x)=6

Step 3: Solve this new equation.

3x+2(6−x)=6

3x+12−2x=6

collecting like terms we have;

3x-2x=6-12

x= -6

Step 4: Solve for the second variable

y=6−x,since x = -6

y=6-(-6)

y= 6+6=12

The solution is: (x, y) = (-6, 12)