Solve the system of linear equations by the substitution method.
C) No solution. The system is inconsistent.

Question

Solve the system of linear equations by the substitution method. 
C) No solution. The system is inconsistent.

Quizplus · Accepted Answer

From the first equation, we can solve for x:

4x + y = 13 
4x = 13 - y 
x = (13 - y)/4

Substitute this expression for x into the second equation:

2( (13-y)/4 ) - y = -1

Simplify:

(13 - y)/2 - y = -1 
13 - y - 2y = -2 
-3y = -15 
y = 5

Now substitute y = 5 back into either equation to solve for x:

4x + 5 = 13 
4x = 8 
x = 2

Therefore, the solution is (2,5), which matches choice B.

Solve the System of Linear Equations by the Substitution Method