To eliminate the [tex]\( y \)[/tex] term from the given system of equations, we need to arrange the equations in such a way that when we perform an operation on them, the [tex]\( y \)[/tex] terms cancel each other out. Here are the given equations:
[tex]\[
\begin{array}{l}
15x + 7y = 4 \\
5x + 7y = 2
\end{array}
\][/tex]
To eliminate the [tex]\( y \)[/tex] term, we can subtract the second equation from the first. Let's do this step by step.
First, write down the system of equations clearly:
1. [tex]\( 15x + 7y = 4 \)[/tex]
2. [tex]\( 5x + 7y = 2 \)[/tex]
Step 1: Subtract the second equation from the first:
[tex]\[ (15x + 7y) - (5x + 7y) = 4 - 2 \][/tex]
Step 2: Simplify the left-hand and right-hand sides of the resulting equation:
The left-hand side simplifies as follows:
[tex]\[ 15x + 7y - 5x - 7y \][/tex]
Since [tex]\( +7y \)[/tex] and [tex]\( -7y \)[/tex] cancel each other out, we are left with:
[tex]\[ 15x - 5x = 10x \][/tex]
The right-hand side simplifies to:
[tex]\[ 4 - 2 = 2 \][/tex]
So, the simplified equation is:
[tex]\[ 10x = 2 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{2}{10} \][/tex]
[tex]\[ x = 0.2 \][/tex]
Therefore, after eliminating the [tex]\( y \)[/tex] term and solving the simplified one-variable equation, we find:
[tex]\[ x = 0.2 \][/tex]
