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Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps.

Let [tex]\( x \)[/tex] represent the number of domestic stamps and [tex]\( y \)[/tex] represent the number of foreign stamps.

This system of equations models the given information:

[tex]\[
\begin{array}{l}
x - y = 34 \\
x + y = 212
\end{array}
\][/tex]

Solve the system of equations.

How many foreign stamps does Malik have?
[tex]\(\boxed{} \)[/tex] foreign stamps

How many domestic stamps does Malik have?
[tex]\(\boxed{} \)[/tex] domestic stamps



Answer :

GinnyAnswer
Sure, let's solve this system of equations step by step.

We start with the given system of equations:
[tex]\[ \begin{array}{l} x - y = 34 \\ x + y = 212 \end{array} \][/tex]

To solve this system, we can use the method of elimination or substitution. Here, I'll use the elimination method:

1. Add the two equations together to eliminate [tex]\( y \)[/tex]:
[tex]\[ (x - y) + (x + y) = 34 + 212 \][/tex]
Simplifying the left side, we get:
[tex]\[ 2x = 246 \][/tex]
Solving for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ x = 123 \][/tex]

2. Substitute [tex]\( x = 123 \)[/tex] back into one of the original equations to solve for [tex]\( y \)[/tex]:
Let's use the second equation [tex]\( x + y = 212 \)[/tex]:
[tex]\[ 123 + y = 212 \][/tex]
Solving for [tex]\( y \)[/tex] by subtracting 123 from both sides:
[tex]\[ y = 89 \][/tex]

Thus, Malik has [tex]\( \boxed{89} \)[/tex] foreign stamps and [tex]\( \boxed{123} \)[/tex] domestic stamps.

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