Question

graph the system on a separate sheet of paper and determine the number of solutions it has. if it has one solution, determine its coordinates.$y = -2x + 1$$2x + y = -1$a) no solutionb) 1 solution; $(2,-3)$c) infinitely many solutionsd) 1 solution; $(-1,1)$

Explanation:

Step1: Substitute $y$ into linear equation

Substitute $y=-2x+1$ into $2x+y=-1$:
$2x + (-2x + 1) = -1$

Step2: Simplify and solve for $x$

Simplify the left-hand side:
$2x - 2x + 1 = -1$
$1 = -1$

Step3: Analyze the result

The simplified equation $1=-1$ is a contradiction, meaning there is no value of $x$ (or $y$) that satisfies both equations simultaneously.

Answer:

A) no solution