Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Let’s solve the given system of equations step-by-step.
The given system of equations is:
[tex]\[ x + \frac{6}{y} - 7 = 0 \][/tex]
[tex]\[ 2xy + 4 = 10y \][/tex]
Step 1: Solve the first equation for [tex]\( x \)[/tex]
Rewrite the first equation as:
[tex]\[ x + \frac{6}{y} = 7 \][/tex]
Subtract [tex]\(\frac{6}{y}\)[/tex] from both sides:
[tex]\[ x = 7 - \frac{6}{y} \][/tex]
Step 2: Substitute [tex]\( x \)[/tex] from the first equation into the second equation
The second equation is:
[tex]\[ 2xy + 4 = 10y \][/tex]
Substitute [tex]\( x = 7 - \frac{6}{y} \)[/tex] into the second equation:
[tex]\[ 2\left(7 - \frac{6}{y}\right)y + 4 = 10y \][/tex]
Step 3: Simplify and solve for [tex]\( y \)[/tex]
Distribute [tex]\( y \)[/tex]:
[tex]\[ 2(7y - 6) + 4 = 10y \][/tex]
[tex]\[ 14y - 12 + 4 = 10y \][/tex]
Combine like terms:
[tex]\[ 14y - 8 = 10y \][/tex]
Subtract [tex]\( 10y \)[/tex] from both sides:
[tex]\[ 4y - 8 = 0 \][/tex]
Add 8 to both sides:
[tex]\[ 4y = 8 \][/tex]
Divide both sides by 4:
[tex]\[ y = 2 \][/tex]
Step 4: Substitute [tex]\( y \)[/tex] back into the expression for [tex]\( x \)[/tex]
[tex]\[ x = 7 - \frac{6}{y} \][/tex]
Substitute [tex]\( y = 2 \)[/tex]:
[tex]\[ x = 7 - \frac{6}{2} \][/tex]
[tex]\[ x = 7 - 3 \][/tex]
[tex]\[ x = 4 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ (x, y) = (4, 2) \][/tex]
The given system of equations is:
[tex]\[ x + \frac{6}{y} - 7 = 0 \][/tex]
[tex]\[ 2xy + 4 = 10y \][/tex]
Step 1: Solve the first equation for [tex]\( x \)[/tex]
Rewrite the first equation as:
[tex]\[ x + \frac{6}{y} = 7 \][/tex]
Subtract [tex]\(\frac{6}{y}\)[/tex] from both sides:
[tex]\[ x = 7 - \frac{6}{y} \][/tex]
Step 2: Substitute [tex]\( x \)[/tex] from the first equation into the second equation
The second equation is:
[tex]\[ 2xy + 4 = 10y \][/tex]
Substitute [tex]\( x = 7 - \frac{6}{y} \)[/tex] into the second equation:
[tex]\[ 2\left(7 - \frac{6}{y}\right)y + 4 = 10y \][/tex]
Step 3: Simplify and solve for [tex]\( y \)[/tex]
Distribute [tex]\( y \)[/tex]:
[tex]\[ 2(7y - 6) + 4 = 10y \][/tex]
[tex]\[ 14y - 12 + 4 = 10y \][/tex]
Combine like terms:
[tex]\[ 14y - 8 = 10y \][/tex]
Subtract [tex]\( 10y \)[/tex] from both sides:
[tex]\[ 4y - 8 = 0 \][/tex]
Add 8 to both sides:
[tex]\[ 4y = 8 \][/tex]
Divide both sides by 4:
[tex]\[ y = 2 \][/tex]
Step 4: Substitute [tex]\( y \)[/tex] back into the expression for [tex]\( x \)[/tex]
[tex]\[ x = 7 - \frac{6}{y} \][/tex]
Substitute [tex]\( y = 2 \)[/tex]:
[tex]\[ x = 7 - \frac{6}{2} \][/tex]
[tex]\[ x = 7 - 3 \][/tex]
[tex]\[ x = 4 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ (x, y) = (4, 2) \][/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.