Question

Solve the system of equations

y= -x+3 and 2x+2y=6

a) there are no solutions

b) the solution is (2, -1)

c) there are infinitely many solutions

d) the solution is (-1, 3)

Answer 1

c) there are infinitely many solutions

Step-by-step explanation:

Add x to the first equation to put it in standard form:

... x + y = 3

Divide the second equation by the common factor of all terms, 2, to put it in standard form:

... x + y = 3

These two equations describe the same line. Every point on the line is a solution to both equations, so there are infinitely many solutions. (We say these equations are "dependent.")