Question 685·Medium·Algebra

0 / 700

\begin{aligned} y &< 2x - 1 \\[1.4em] x &\ge -1 \end{aligned}

Which of the following ordered pairs $(x, y)$ is a solution to the system of inequalities above?

A system of inequalities asks for a point that meets every rule at once. Graph both inequalities in Desmos, then plot the answer choices. The solution must lie in both shaded regions. Watch the boundary: a strict $<$ excludes points on its dotted line, even if they meet the other rule.

Hints

Hint 1
Each inequality shades the points that satisfy it. For a system, look where the shadings overlap; a point in only one shaded region doesn't satisfy the whole system.
Hint 2
The boundary of $y<2x-1$ is $y=2x-1$ . Because $<$ is strict, a point on that line doesn't count, even if it satisfies $x\ge-1$ .

Step-by-step

Graph the overlap in Desmos
Step 1
Graph both inequalities
Type $y<2x-1$ and $x\ge-1$ on separate Desmos lines. The first shades below its dotted boundary line, while the second shades to the right of $x=-1$ and includes that solid line. The overlap contains the points that meet both rules.
Step 2
Plot the choices and check the overlap
Plot each choice on its own line. Desmos shows only $(0,-3)$ in both shadings. Its coordinates confirm this: $-3<2(0)-1=-1$ and $0\ge-1$ . Don't count $(-1,-3)$ : it lies on the dotted line because $-3=2(-1)-1$ , and $<$ excludes equality. So $(0,-3)$ solves the system. Choice B.

Question 685·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this