Question

svlc algebra 1a - standard (15260)
solving systems of linear
inequalities

which ordered pair makes both inequalities true?
y ≤ -x + 1
y > x

(-3, 5) (0, -1)
(-1, -3) (-2, 2)

Explanation:

Step1: Check each ordered pair in \( y \leq -x + 1 \) and \( y > x \)

For \((-3, 5)\):

• Check \( y \leq -x + 1 \): Substitute \( x = -3 \), \( y = 5 \). \( 5 \leq -(-3)+1 = 3 + 1 = 4 \)? \( 5 \leq 4 \) is false.

For \((0, -1)\):

• Check \( y > x \): \( -1 > 0 \)? False.

For \((-1, -3)\):

• Check \( y > x \): \( -3 > -1 \)? False.

For \((-2, 2)\):

• Check \( y \leq -x + 1 \): Substitute \( x = -2 \), \( y = 2 \). \( 2 \leq -(-2)+1 = 2 + 1 = 3 \)? \( 2 \leq 3 \) is true.
• Check \( y > x \): \( 2 > -2 \)? True.

Answer:

\((-2, 2)\)