Question

② x = -4y + 8
4x + 5y = -1
③ y = 3x + 4
x + y = 8

Explanation:

(for system ②):

Step1: Substitute $x=-4y+8$ into $4x+5y=-1$

$4(-4y+8)+5y=-1$

Step2: Expand and simplify

$-16y+32+5y=-1$
$-11y+32=-1$

Step3: Solve for $y$

$-11y=-1-32$
$-11y=-33$
$y=\frac{-33}{-11}=3$

Step4: Substitute $y=3$ into $x=-4y+8$

$x=-4(3)+8=-12+8=-4$

(for system ③):

Step1: Substitute $y=3x+4$ into $x+y=8$

$x+(3x+4)=8$

Step2: Combine like terms

$4x+4=8$

Step3: Solve for $x$

$4x=8-4$
$4x=4$
$x=\frac{4}{4}=1$

Step4: Substitute $x=1$ into $y=3x+4$

$y=3(1)+4=3+4=7$

Answer:

For system ②: $x=-4$, $y=3$
For system ③: $x=1$, $y=7$