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)
