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

Answer :

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.

CATTUSCACTUSGO

[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]

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