Question

Identify the type of system y=-x+42x+2y=8is Equivalen, incontinent, independent.?

Answer 1

Step 1:

There are three types of systems of linear equations in two variables, and three types of solutions.

1. An independent system has exactly one solution pair. The point where the two lines intersect is the only solution.

2. An inconsistent system has no solution.

3. A dependent system has infinitely many solutions.

Step 2

Solve the systems of the equations using the substitution method

`\begin{gathered} \text{y = -x + 4} \\ 2x\text{ + 2y = 8} \\ 2x\text{ + 2\lparen-x + 4\rparen = 8} \\ 2x\text{ - 2x + 8 = 8} \\ 8\text{ = 8} \end{gathered}`

Final answer

The system is dependent so there are infinite solutions.

Equivalent