Question

svlc algebra 1a - standard (15260)
solving systems of linear inequalities
identifying the solution to a system of two - variable inequalities
which equation represents an inequality in the system of inequalities shown in the graph?
which point is a solution to the system?

Explanation:

To solve this, we first analyze the lines:

Step 1: Identify the equations of the lines

• Red line (solid): Passes through \((0, -1)\) and \((1, 0)\) (slope \(m = 1\)). Equation: \(y = x - 1\). Since it’s solid and the shaded region is above, inequality: \(y \geq x - 1\) (or \(y > x - 1\) if dashed, but here solid, so \(\geq\)).
• Dashed line (blue): Passes through \((0, 2)\) and \((-1, 0)\) (slope \(m = 2\)). Equation: \(y = 2x + 2\). Since it’s dashed and the shaded region is below, inequality: \(y < 2x + 2\).

Step 2: Find a solution point

A solution must satisfy both inequalities. Let’s test \((0, 0)\):

• For \(y \geq x - 1\): \(0 \geq 0 - 1\) (true, \(0 \geq -1\)).
• For \(y < 2x + 2\): \(0 < 2(0) + 2\) (true, \(0 < 2\)).

Final Answers

1. An inequality in the system: \(\boldsymbol{y \geq x - 1}\) (or \(y < 2x + 2\), depending on the options).
2. A solution point: \(\boldsymbol{(0, 0)}\) (or other valid point like \((1, 1)\), etc.).

Answer:

To solve this, we first analyze the lines:

Step 1: Identify the equations of the lines

• Red line (solid): Passes through \((0, -1)\) and \((1, 0)\) (slope \(m = 1\)). Equation: \(y = x - 1\). Since it’s solid and the shaded region is above, inequality: \(y \geq x - 1\) (or \(y > x - 1\) if dashed, but here solid, so \(\geq\)).
• Dashed line (blue): Passes through \((0, 2)\) and \((-1, 0)\) (slope \(m = 2\)). Equation: \(y = 2x + 2\). Since it’s dashed and the shaded region is below, inequality: \(y < 2x + 2\).

Step 2: Find a solution point

A solution must satisfy both inequalities. Let’s test \((0, 0)\):

• For \(y \geq x - 1\): \(0 \geq 0 - 1\) (true, \(0 \geq -1\)).
• For \(y < 2x + 2\): \(0 < 2(0) + 2\) (true, \(0 < 2\)).

Final Answers

1. An inequality in the system: \(\boldsymbol{y \geq x - 1}\) (or \(y < 2x + 2\), depending on the options).
2. A solution point: \(\boldsymbol{(0, 0)}\) (or other valid point like \((1, 1)\), etc.).