Question

1. which standard form equation is formed from the two equations?

$x + 2 = 5$ and $y - 3 = 2$
$x - y = -2$
$x + y = 2$
$x + y = -2$
$x - y = 2$

1. which standard form equation is formed from the two equations?

$2x - 3 > 4$ and $y + 2 < 1$
$2x + y > 8$
$2x - y < 7$
$2x + y > 7$
$2x - y > 8$

Explanation:

Question 5

Step1: Solve for \( x \) and \( y \)

For \( x + 2 = 5 \), subtract 2 from both sides: \( x = 5 - 2 = 3 \).
For \( y - 3 = 2 \), add 3 to both sides: \( y = 2 + 3 = 5 \).

Step2: Substitute \( x \) and \( y \) into options

Check each option:

• \( x - y = 3 - 5 = -2 \), which matches \( x - y = -2 \).
• \( x + y = 3 + 5 = 8

eq 2 \).

• \( x + y = 8

eq -2 \).

• \( x - y = -2

eq 2 \).

Step1: Solve each inequality for standard form

For \( 2x - 3 > 4 \), add 3 to both sides: \( 2x > 7 \).
For \( y + 2 < 1 \), subtract 2 from both sides: \( y < -1 \), or \( -y > 1 \) (multiply by -1, reverse inequality).

Step2: Combine inequalities

Add \( 2x > 7 \) and \( -y > 1 \): \( 2x - y > 7 + 1 \), so \( 2x - y > 8 \).

Answer:

\( x - y = -2 \) (the first option)

Question 6