Question

b. \

$$\begin{cases} y = x + 5 \\\\ y = 2x + 9 \\end{cases}$$

for $y = x + 5$ and $y = 2x + 9$, there are two tables with $x$ and $y$ columns. the $x$ values in both tables are -5, -4, -3, -2, -1, 0, 1, 2, 3, and the $y$ values are blank to be filled.

Explanation:

Step1: Calculate $y$ for $y=x+5$

For each $x$:

• $x=-5$: $y=-5+5=0$
• $x=-4$: $y=-4+5=1$
• $x=-3$: $y=-3+5=2$
• $x=-2$: $y=-2+5=3$
• $x=-1$: $y=-1+5=4$
• $x=0$: $y=0+5=5$
• $x=1$: $y=1+5=6$
• $x=2$: $y=2+5=7$
• $x=3$: $y=3+5=8$

Step2: Calculate $y$ for $y=2x+9$

For each $x$:

• $x=-5$: $y=2(-5)+9=-10+9=-1$
• $x=-4$: $y=2(-4)+9=-8+9=1$
• $x=-3$: $y=2(-3)+9=-6+9=3$
• $x=-2$: $y=2(-2)+9=-4+9=5$
• $x=-1$: $y=2(-1)+9=-2+9=7$
• $x=0$: $y=2(0)+9=0+9=9$
• $x=1$: $y=2(1)+9=2+9=11$
• $x=2$: $y=2(2)+9=4+9=13$
• $x=3$: $y=2(3)+9=6+9=15$

Step3: Find system solution

Find matching $(x,y)$ pairs:
From tables, $x=-4$, $y=1$ is common.
Verify: $1=-4+5$ and $1=2(-4)+9$, both true.

Answer:

Completed table for $y=x+5$:

$x$	$y$
$-4$	$1$
$-3$	$2$
$-2$	$3$
$-1$	$4$
$0$	$5$
$1$	$6$
$2$	$7$
$3$	$8$

Completed table for $y=2x+9$:

$x$	$y$
$-4$	$1$
$-3$	$3$
$-2$	$5$
$-1$	$7$
$0$	$9$
$1$	$11$
$2$	$13$
$3$	$15$

Solution to the system:

$x=-4$, $y=1$