Question

score: 3.25/5 penalty: 0.25 off
question
find the value of x, y, and z, in the rhombus below.
answer attempt 1 out of 2
x =
y =
z =

Explanation:

Step1: Use the property of a rhombus (all sides are equal)

In a rhombus, all sides are equal. So we have the following equations:

• $6x - 1=8y$
• $8y=- 3z - 1$
• $6x - 1=7y - 2$

Step2: Solve the first - third equation for $y$

From $6x - 1=7y - 2$ and $6x - 1=8y$, we substitute $6x - 1$ in the first equation with $8y$ in the second equation.
$8y=7y - 2$
Subtract $7y$ from both sides: $8y-7y=7y - 2-7y$
$y=\frac{7}{8}$

Step3: Solve for $x$

Substitute $y = \frac{7}{8}$ into $6x - 1=8y$
$6x - 1=8\times\frac{7}{8}$
$6x - 1 = 7$
Add $1$ to both sides: $6x-1 + 1=7 + 1$
$6x=8$
Divide both sides by $6$: $x=\frac{8}{6}=\frac{3}{2}$

Step4: Solve for $z$

Substitute $y=\frac{7}{8}$ into $8y=-3z - 1$
$8\times\frac{7}{8}=-3z - 1$
$7=-3z - 1$
Add $1$ to both sides: $7 + 1=-3z-1 + 1$
$8=-3z$
Divide both sides by $-3$: $z=-3$

Answer:

$x = \frac{3}{2}$, $y = \frac{7}{8}$, $z = -3$