Let's solve this system of linear equations step by step. The given equations are:
1. [tex]\(x - y = 34\)[/tex] [tex]\(\quad \text{(Equation 1)}\)[/tex]
2. [tex]\(x + y = 212\)[/tex] [tex]\(\quad \text{(Equation 2)}\)[/tex]
Where:
- [tex]\(x\)[/tex] represents the number of domestic stamps.
- [tex]\(y\)[/tex] represents the number of foreign stamps.
### Step-by-Step Solution:
Step 1: Add the Two Equations
First, we'll add Equation 1 and Equation 2 to eliminate [tex]\(y\)[/tex]:
[tex]\[
(x - y) + (x + y) = 34 + 212
\][/tex]
This simplifies to:
[tex]\[
2x = 246
\][/tex]
Step 2: Solve for [tex]\(x\)[/tex]
Next, we'll solve for [tex]\(x\)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{246}{2} = 123
\][/tex]
So, the number of domestic stamps [tex]\(x = 123\)[/tex].
Step 3: Solve for [tex]\(y\)[/tex]
Now, we use Equation 2 to solve for [tex]\(y\)[/tex]:
[tex]\[
x + y = 212
\][/tex]
Substitute [tex]\(x = 123\)[/tex] into the equation:
[tex]\[
123 + y = 212
\][/tex]
Subtract 123 from both sides:
[tex]\[
y = 212 - 123
\][/tex]
This simplifies to:
[tex]\[
y = 89
\][/tex]
So, the number of foreign stamps [tex]\(y = 89\)[/tex].
### Final Answer:
- Number of foreign stamps Malik has: [tex]\( \boxed{89} \)[/tex] foreign stamps.
- Number of domestic stamps Malik has: [tex]\( \boxed{123} \)[/tex] domestic stamps.
