Question

$4x + 6y + 5z = 90$
$4x + 6y = 60$
$3x = 18$

$x + 3 + 4z = 36$
$x + 3y = 24$
$4x = 24$

Explanation:

Step1: Solve for $x$ (top set)

From $3x=18$, divide by 3:
$\frac{3x}{3}=\frac{18}{3}$
$x=6$

Step2: Solve for $y$ (top set)

Substitute $x=6$ into $4x+6y=60$:
$4(6)+6y=60$
$24+6y=60$
$6y=60-24=36$
$\frac{6y}{6}=\frac{36}{6}$
$y=6$

Step3: Solve for $z$ (top set)

Substitute $4x+6y=60$ into $4x+6y+5z=90$:
$60+5z=90$
$5z=90-60=30$
$\frac{5z}{5}=\frac{30}{5}$
$z=6$

Step4: Solve for $x$ (bottom set)

From $4x=24$, divide by 4:
$\frac{4x}{4}=\frac{24}{4}$
$x=6$

Step5: Solve for $y$ (bottom set)

Substitute $x=6$ into $x+3y=24$:
$6+3y=24$
$3y=24-6=18$
$\frac{3y}{3}=\frac{18}{3}$
$y=6$

Step6: Solve for $z$ (bottom set)

Substitute $x=6$ into $x+3+4z=36$:
$6+3+4z=36$
$9+4z=36$
$4z=36-9=27$
$\frac{4z}{4}=\frac{27}{4}$
$z=6.75$

Answer:

Top system solutions: $x=6$, $y=6$, $z=6$
Bottom system solutions: $x=6$, $y=6$, $z=\frac{27}{4}$ (or $6.75$)