IDNLearn.com is designed to help you find reliable answers to any question you have. Discover reliable and timely information on any topic from our network of knowledgeable professionals.
Sagot :
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]
[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]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.