Question

30 POINTS! What is the first step to solve the following system of equations using substitution?

Answer 1

Answer:

add the 2 equations together

Answer 2

Answer:

The answer to your question would be C.

Step-by-step explanation:

Substitution method can be applied in four steps

Step 1:

Solve one of the equations for either x = or y = .

Step 2:

Substitute the solution from step 1 into the other equation.

Step 3:

Solve this new equation.

Step 4:

Solve for the second variable.

Example 1: Solve the following system by substitution

2x+3yx+y=5=5

Solution:

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

x+yy=5=5−x

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

2x+3y2x+3(5−x)=5=5

Step 3: Solve this new equation.

2x+3(5−x)2x+15−3x−x+15−xx=5=5=5=5−15=10

Step 4: Solve for the second variable

yyy=5−x=5−10=−5

The solution is: (x, y) = (10, -5)

Note: It does not matter which equation we choose first and which second. Just choose the most convenient one first!

Example 2: Solve by substitution

2x+5y4x−y=12=2

Solution:

Step 1: Solve one of the equations for either x = or y =. Since the coefficient of y in equation 2 is -1, it is easiest to solve for y in equation 2.

4x−y−yy=2=2−4x=4x−2

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

2x+5y2x+5(4x−2)=12=12

Step 3: Solve this new equation ( for x ).

2x+5(4x−2)2x+2x+20x−1022xx=12=12=22=1

Step 4: Solve for the second variable

yyy=4x−2=4⋅x−2=2

The solution is: (x,y)=(1,2)