Question

Given the following system identify the type of system x+y=4x-y=6

Answer 1

Given the question, the following are the solution steps to answer the question.

STEP 1: Write the given system of equation

`\begin{gathered} x+y=4----equation\text{ 1} \\ x-y=6-----equation\text{ 2} \end{gathered}`

STEP 2: Solve the given equation

Subtract equation 2 from equation 1

`\begin{gathered} (x-x)+(y-(-y))=4-6 \\ y+y=-2 \\ 2y=-2 \\ Divide\text{ both sides by 2} \\ (2y)/(2)=-(2)/(2) \\ y=-1 \end{gathered}`

STEP 3: Solve for x

`\begin{gathered} Substitute\text{ -1 for y in equation 1} \\ x+(-1)=4 \\ x-1=4 \\ x=4+1 \\ x=5 \end{gathered}`

The values of x and y are 5 and -1 respectively meaning that the system has one solution, hence the type of system of equation given is a CONSISTENT system of linear equation.