To solve the system of linear equations:
[tex]\[
\begin{cases}
3c + 2s = 8.75 \\
2c + 4s = 8.5
\end{cases}
\][/tex]
we can follow a step-by-step method. Let's use the substitution or elimination method to solve these equations.
### Step 1: Write down the equations
We have:
1. [tex]\(3c + 2s = 8.75\)[/tex]
2. [tex]\(2c + 4s = 8.5\)[/tex]
### Step 2: Simplify the equations if possible
Notice that the second equation can be simplified by dividing everything by 2:
[tex]\[
2c + 4s = 8.5 \implies c + 2s = 4.25
\][/tex]
Now we have the simplified system:
[tex]\[
\begin{cases}
3c + 2s = 8.75 \\
c + 2s = 4.25
\end{cases}
\][/tex]
### Step 3: Eliminate one variable by subtracting the equations
To eliminate [tex]\(s\)[/tex], we can subtract the second simplified equation from the first equation:
[tex]\[
(3c + 2s) - (c + 2s) = 8.75 - 4.25
\][/tex]
Simplifying this:
[tex]\[
3c + 2s - c - 2s = 4.5
\][/tex]
[tex]\[
2c = 4.5
\][/tex]
### Step 4: Solve for [tex]\(c\)[/tex]
To find [tex]\(c\)[/tex], divide both sides by 2:
[tex]\[
c = \frac{4.5}{2} = 2.25
\][/tex]
### Step 5: Substitute [tex]\(c\)[/tex] back into one of the equations to solve for [tex]\(s\)[/tex]
Using the simplified second equation [tex]\(c + 2s = 4.25\)[/tex]:
[tex]\[
2.25 + 2s = 4.25
\][/tex]
Subtract [tex]\(2.25\)[/tex] from both sides:
[tex]\[
2s = 4.25 - 2.25
\][/tex]
[tex]\[
2s = 2
\][/tex]
Divide both sides by 2:
[tex]\[
s = \frac{2}{2} = 1
\][/tex]
### Step 6: Conclusion
The solution to the system of equations is:
[tex]\[
c = 2.25
\][/tex]
[tex]\[
s = 1
\][/tex]
Hence, the cost of a slice of cheese pizza [tex]\(c\)[/tex] is [tex]$2.25 and the cost of a soda \(s\) is $[/tex]1.00.
