Answered

Get detailed and reliable answers to your questions with IDNLearn.com. Join our Q&A platform to receive prompt and accurate responses from knowledgeable professionals in various fields.

Solve the system of equations:

[tex]\[ \begin{array}{l}
3x + y = 2x + 3y \\
2x + 3y = x + y + 44
\end{array} \][/tex]

Sagot :

GinnyAnsweridn
Let's solve the given system of equations step-by-step:

[tex]\[ \begin{array}{l} 1) \, 3x + y = 2x + 3y \\ 2) \, 2x + 3y = x + y + 44 \\ \end{array} \][/tex]

Step 1: Solve the first equation

[tex]\[ 3x + y = 2x + 3y \][/tex]

Subtract [tex]\(2x\)[/tex] and [tex]\(y\)[/tex] from both sides:

[tex]\[ 3x - 2x + y - y = 2x - 2x + 3y - y \][/tex]

This simplifies to:

[tex]\[ x = 2y \][/tex]

Step 2: Substitute [tex]\( x = 2y \)[/tex] into the second equation

[tex]\[ 2x + 3y = x + y + 44 \][/tex]

Replace [tex]\( x \)[/tex] with [tex]\( 2y \)[/tex]:

[tex]\[ 2(2y) + 3y = 2y + y + 44 \][/tex]

Simplify:

[tex]\[ 4y + 3y = 2y + y + 44 \][/tex]

Combine like terms:

[tex]\[ 7y = 3y + 44 \][/tex]

Subtract [tex]\( 3y \)[/tex] from both sides:

[tex]\[ 7y - 3y = 44 \][/tex]

This simplifies to:

[tex]\[ 4y = 44 \][/tex]

Divide both sides by 4:

[tex]\[ y = 11 \][/tex]

Step 3: Substitute [tex]\( y = 11 \)[/tex] back into [tex]\( x = 2y \)[/tex]

[tex]\[ x = 2(11) \][/tex]

This simplifies to:

[tex]\[ x = 22 \][/tex]

Solution:

The values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations are:

[tex]\[ x = 22 \][/tex]
[tex]\[ y = 11 \][/tex]

Thus, the solution to the system of equations is [tex]\( (22, 11) \)[/tex].
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.