zerahmannah23
Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

solve the simultaneous linear equation 2x+5y=11, 7x+4y=2​

Sagot :

Answer:

x = -[tex]\frac{34}{27}[/tex] and y = [tex]\frac{73}{27}[/tex]

Step-by-step explanation:

2x + 5y = 11

7x + 4y = 2

Let's try elimination here since we have a system of equations:

-7(2x + 5y = 11) = -14x - 35y = -77

and

2(7x + 4y = 2) = 14x + 8y = 4

The x's cancel out now so let's combine the two equations:

-35 + 8 = -27

-77 + 4 = -73

-27y = -73

y = [tex]\frac{73}{27}[/tex]

Now that we have y's value, let's plug that value in for y in the other equation. You may choose whichever equation you want to solve for x but it is recommended to use the easiest one. (Since this value is complicated, it won't really matter.)

2x + 5([tex]\frac{73}{27}[/tex]) = 11

2x + [tex]\frac{365}{27}[/tex] = 11

2x = -[tex]\frac{68}{27}[/tex]

x = -[tex]\frac{34}{27}[/tex]

To check and make sure you have the correct values, plug both values into the orginal equation and make sure the equation is true.

CattusCactus

[tex]{\tt{2x + 5y = 11}}[/tex]

[tex]{\tt{7x + 4y = 2}}[/tex]

[tex] \: \: [/tex]

[tex]{\tt{2x = 11 - 5y}}[/tex]

[tex]{\tt{7x = 2 - 4y}}[/tex]

[tex] \: \: [/tex]

[tex]{\tt{x = ( 11 - 5y ) ÷ 2}}[/tex]

[tex]{\tt{x = \frac{11}{2} - \frac{5}{2} y}}[/tex]

[tex] \: \: [/tex]

[tex]{\tt{x = ( 2 - 4y ) ÷ 7}}[/tex]

[tex]{\tt{x = \frac{2}{7} - \frac{4}{7} y}}[/tex]

[tex] \: \: [/tex]

_____________________

[tex] \: \: [/tex]

[tex] \: \: \: \: \: \: {\tt{ \frac{11}{2} - \frac{5}{2} y = \frac{2}{7} - \frac{4}{7} y\: \: ( \times14)}}[/tex]

[tex] \: \: \: \: {\tt{77 - 35y = 4 - 8y}}[/tex]

[tex]{\tt{ - 35y + 8y = 4 - 77}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: {\tt{ - 27y = - 73}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\tt{y = \frac{73}{27} }}[/tex]

[tex] \: \: [/tex]

SUBSTITUTION

[tex] \: \: [/tex]

[tex]{\tt{x = \frac{2}{7} - \frac{4}{7} \times \frac{73}{27} }}[/tex]

[tex]{\tt{x = - \frac{34}{27} }}[/tex]

[tex] \: \: [/tex]

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.