Solve the following inequality graphically in | vedclass

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Question

(A) Step $1$: Consider the corresponding equation $2x + y = 3$. Step $2$: Find the intercepts to plot the line. If $x = 0$,$y = 3$. If $y = 0$,$x = 1.

Vedclass · Accepted Answer

The region above the line $2x + y = 3$.

Vedclass · Answer

(A) Step $1$: Consider the corresponding equation $2x + y = 3$. Step $2$: Find the intercepts to plot the line. If $x = 0$,$y = 3$. If $y = 0$,$x = 1.5$. The line passes through $(0, 3)$ and $(1.5, 0)$. Step $3$: Since the inequality is strictly greater than $(>)$,draw the line as a dashed line to indicate that points on the line are not included in the solution. Step $4$: Test a point not on the line,such as $(0, 0)$. Substituting into the inequality: $2(0) + 0 > 3$,which simplifies to $0 > 3$. This is false. Step $5$: Since the test point $(0, 0)$ does not satisfy the inequality,the solution region is the half-plane that does not contain the origin. Thus,the solution is the region above the line $2x + y = 3$.

Solve the following inequality graphically in a two-dimensional plane: $2x + y > 3$.

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