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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.

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

1. How many foreign stamps does Malik have? [tex]\(\square\)[/tex] foreign stamps

2. How many domestic stamps does Malik have? [tex]\(\square\)[/tex] domestic stamps



Answer :

GinnyAnswer
To solve this system of equations, we need to find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously.

The system of equations given is:
[tex]\[ \begin{array}{l} x - y = 34 \\ x + y = 212 \end{array} \][/tex]

Let's solve this step-by-step.

1. Add the two equations to eliminate [tex]\(y\)[/tex]:
[tex]\[ \begin{array}{c} (x - y) + (x + y) = 34 + 212 \\ \end{array} \][/tex]

Simplify the left side:
[tex]\[ x - y + x + y = 34 + 212 \][/tex]

Combine like terms:
[tex]\[ 2x = 246 \][/tex]

Solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{246}{2} = 123 \][/tex]

So, Malik has 123 domestic stamps.

2. Substitute [tex]\(x = 123\)[/tex] back into one of the original equations to find [tex]\(y\)[/tex]:

We use the second equation:
[tex]\[ x + y = 212 \][/tex]

Plug in [tex]\(x = 123\)[/tex]:
[tex]\[ 123 + y = 212 \][/tex]

Solve for [tex]\(y\)[/tex]:
[tex]\[ y = 212 - 123 = 89 \][/tex]

So, Malik has 89 foreign stamps.

Therefore, Malik has:
[tex]\[ \boxed{89} \][/tex]
foreign stamps and
[tex]\[ \boxed{123} \][/tex]
domestic stamps.

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