Let's solve the system of linear equations given by:
[tex]\[
\begin{cases}
4s + 2j = 64 \\
3s + 3j = 72
\end{cases}
\][/tex]
Where [tex]\( s \)[/tex] represents the price of one shirt and [tex]\( j \)[/tex] represents the price of one pair of jeans.
### Step 1: Simplify the equations if possible.
The second equation is:
[tex]\[ 3s + 3j = 72 \][/tex]
We can divide the entire equation by 3 to simplify it:
[tex]\[ s + j = 24 \][/tex]
Now, we have:
[tex]\[
\begin{cases}
4s + 2j = 64 \\
s + j = 24
\end{cases}
\][/tex]
### Step 2: Solve the simpler system of equations.
From the simplified second equation:
[tex]\[ s + j = 24 \][/tex]
we can express [tex]\( j \)[/tex] in terms of [tex]\( s \)[/tex]:
[tex]\[ j = 24 - s \][/tex]
### Step 3: Substitute the expression from Step 2 into the first equation.
Substitute [tex]\( j = 24 - s \)[/tex] into the first equation:
[tex]\[ 4s + 2(24 - s) = 64 \][/tex]
### Step 4: Solve for [tex]\( s \)[/tex].
Expand and simplify the equation:
[tex]\[ 4s + 48 - 2s = 64 \][/tex]
Combine like terms:
[tex]\[ 2s + 48 = 64 \][/tex]
Subtract 48 from both sides:
[tex]\[ 2s = 16 \][/tex]
Divide by 2:
[tex]\[ s = 8 \][/tex]
So, the price of one shirt is [tex]\( s = 8 \)[/tex].
### Step 5: Solve for [tex]\( j \)[/tex] using the value of [tex]\( s \)[/tex].
Substitute [tex]\( s = 8 \)[/tex] back into the simplified second equation [tex]\( s + j = 24 \)[/tex]:
[tex]\[ 8 + j = 24 \][/tex]
Subtract 8 from both sides:
[tex]\[ j = 16 \][/tex]
So, the price of one pair of jeans is [tex]\( j = 16 \)[/tex].
### Final solution:
- The price of one shirt is [tex]\( 8 \)[/tex] units.
- The price of one pair of jeans is [tex]\( 16 \)[/tex] units.
Therefore, one shirt costs 8 units and one pair of jeans costs 16 units.
