Use the substitution method to solve the following system of linear equations:

x + y = 6
x = –y + 2

A.
The solution is (4, 2).

B.
There are an infinite number of solutions.

C.
There is no solution.

D.
The solution is (2, 4).

Question

Use the substitution method to solve the following system of linear equations: 

x + y = 6 
x = –y + 2 

A. 
The solution is (4, 2). 

B. 
There are an infinite number of solutions. 

C. 
There is no solution. 

D. 
The solution is (2, 4).

btaylor · Answer

Since you know what x is (in terms of y), plug that into the given value of x. So:$$x+y=6 \rightarrow (-y+2)+y=6 \rightarrow y-y+2=6 \rightarrow 2=6 \rightarrow ???$$Since we get an untrue statement (2=6), there is no solution, which means that no combination of x and y will result in an equality. Basically if you were to graph the two lines defined by the equation, they are parallel, so they never intersect (at a solution)