To determine the error Malik made, let's carefully consider each step presented and recognize where the mistake occurred.
Given the equation:
[tex]\[
\frac{2}{5} x - 4 y = 10
\][/tex]
The steps are as follows:
1. Substitute a value (substitution step).
2. Simplify the equation by performing operations (arithmetic steps).
3. Isolate the variable and solve it (solving step).
Malik's work is shown as:
[tex]\[
\frac{2}{5} x - 4 y = 10
\][/tex]
[tex]\[
\frac{2}{5} x - 4(60) = 10
\][/tex]
[tex]\[
\frac{2}{5} x - 240 = 10
\][/tex]
[tex]\[
\frac{2}{5} x - 240 + 240 = 10 + 240
\][/tex]
[tex]\[
\frac{5}{2} \left[\frac{2}{5} x\right] = \frac{5}{2} [250]
\][/tex]
[tex]\[
x = 265
\][/tex]
Let's analyze the first main step where Malik substituted the value 60. The initial equation is [tex]\(\frac{2}{5} x - 4 y = 10\)[/tex]. In Malik's solution, the substitution was made:
[tex]\[
\frac{2}{5} x - 4(60) = 10
\][/tex]
Here, 60 was substituted for [tex]\(y\)[/tex]. Since we normally label [tex]\(x\)[/tex] and [tex]\(y\)[/tex] to denote different unknowns, it seems Malik should have kept [tex]\(y\)[/tex] intact and solved for [tex]\(x\)[/tex]. However, Malik has substituted 60 for [tex]\(y\)[/tex] instead of substituting 60 for [tex]\(x\)[/tex].
Therefore, the first error Malik made is in substitution, where Malik substituted 60 for [tex]\(y\)[/tex] instead of [tex]\(x\)[/tex].
So, the correct answer is:
Malik substituted 60 for [tex]\(y\)[/tex] instead of [tex]\(x\)[/tex].
