$$ 28+4 y-z=32 $$ $$ 2 x+14 y+4 z=35 $$ $$ x+3 y+\operatorname{coz}=24 $$ From

Question

UpStudy AI · Accepted Answer

It seems like there might be a typo in your third equation. Specifically, `\operatorname{coz}` is unclear. I'm going to assume that you intended to write `z`. If that's not the case, please let me know!

Given the system of equations:

1. $$ 28 + 4y - z = 32 $$
2. $$ 2x + 14y + 4z = 35 $$
3. $$ x + 3y + z = 24 $$

Let's solve for $$ x $$, $$ y $$, and $$ z $$.

### Step 1: Simplify the First Equation

Start with the first equation:

$$
28 + 4y - z = 32
$$

Subtract 28 from both sides:

$$
4y - z = 4
$$

Solve for $$ z $$:

$$
z = 4y - 4 \quad \text{(Equation 4)}
$$

### Step 2: Substitute $$ z $$ into the Third Equation

Use Equation 4 in the third equation:

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

Substitute $$ z = 4y - 4 $$:

$$
x + 3y + (4y - 4) = 24
$$

Combine like terms:

$$
x + 7y - 4 = 24
$$

Add 4 to both sides:

$$
x + 7y = 28
$$

Solve for $$ x $$:

$$
x = 28 - 7y \quad \text{(Equation 5)}
$$

### Step 3: Substitute $$ z $$ and $$ x $$ into the Second Equation

Use Equations 4 and 5 in the second equation:

$$
2x + 14y + 4z = 35
$$

Substitute $$ x = 28 - 7y $$ and $$ z = 4y - 4 $$:

$$
2(28 - 7y) + 14y + 4(4y - 4) = 35
$$

Expand the terms:

$$
56 - 14y + 14y + 16y - 16 = 35
$$

Combine like terms:

$$
56 - 16 + 16y = 35
$$

$$
40 + 16y = 35
$$

Subtract 40 from both sides:

$$
16y = -5
$$

Divide by 16:

$$
y = -\frac{5}{16}
$$

### Step 4: Find $$ x $$ and $$ z $$

Now, substitute $$ y = -\frac{5}{16} $$ back into Equation 5 to find $$ x $$:

$$
x = 28 - 7\left(-\frac{5}{16}\right) = 28 + \frac{35}{16} = \frac{448}{16} + \frac{35}{16} = \frac{483}{16} = 30\frac{3}{16}
$$

Next, substitute $$ y = -\frac{5}{16} $$ into Equation 4 to find $$ z $$:

$$
z = 4\left(-\frac{5}{16}\right) - 4 = -\frac{20}{16} - 4 = -\frac{5}{4} - 4 = -5.25
$$

### **Solution Summary**

$$
\begin{cases}
x = \dfrac{483}{16} \ (\text{or } 30\frac{3}{16}) \
y = -\dfrac{5}{16} \
z = -\dfrac{21}{4} \ (\text{or } -5.25)
\end{cases}
$$

If the third equation was intended to be different (for example, involving a trigonometric function like $$ \cos z $$), please provide the correct equation so I can assist you accordingly.
The solution to the system of equations is: $$ x = \frac{483}{16} \quad (30\frac{3}{16}), \quad y = -\frac{5}{16}, \quad z = -\frac{21}{4} \quad (-5.25) $$

From

Upstudy AI Solution

Answer

Solution

Step 1: Simplify the First Equation

Step 2: Substitute into the Third Equation

Step 3: Substitute and into the Second Equation

Step 4: Find and

Solution Summary

Mind Expander

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