# Solve the following simultaneous equation:

$

x + y = 8 \\

3x + 4y = 25 \\

$

Answer

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Hint: Find the value of one variable in the form of the other variable from the first equation. Then put it in the second equation.

Complete step-by-step answer:

The given simultaneous equation is:

$

x + y = 8 .....(i) \\

3x + 4y = 25 .....(ii) \\

$

From equation $(i)$, we have:

$

\Rightarrow x + y = 8, \\

\Rightarrow x = 8 - y \\

$

Putting this value in equation $(ii)$, we’ll get:

$

\Rightarrow 3\left( {8 - y} \right) + 4y = 25, \\

\Rightarrow 24 - 3y + 4y = 25, \\

\Rightarrow y = 1 \\

$

Putting $y = 1$ in equation $(i)$, we’ll get:

$

\Rightarrow x + 1 = 8, \\

\Rightarrow x = 7 \\

$

Thus, the solution of the simultaneous equation is $x = 7$ and $y = 1$.

Note: The method used above is called substitution method. We can use another method called addition method. In this method we make the coefficients of any one variable negative of each other in both the equations by multiplying equations with suitable constants. And then add both the equations to get one variable eliminated.

Complete step-by-step answer:

The given simultaneous equation is:

$

x + y = 8 .....(i) \\

3x + 4y = 25 .....(ii) \\

$

From equation $(i)$, we have:

$

\Rightarrow x + y = 8, \\

\Rightarrow x = 8 - y \\

$

Putting this value in equation $(ii)$, we’ll get:

$

\Rightarrow 3\left( {8 - y} \right) + 4y = 25, \\

\Rightarrow 24 - 3y + 4y = 25, \\

\Rightarrow y = 1 \\

$

Putting $y = 1$ in equation $(i)$, we’ll get:

$

\Rightarrow x + 1 = 8, \\

\Rightarrow x = 7 \\

$

Thus, the solution of the simultaneous equation is $x = 7$ and $y = 1$.

Note: The method used above is called substitution method. We can use another method called addition method. In this method we make the coefficients of any one variable negative of each other in both the equations by multiplying equations with suitable constants. And then add both the equations to get one variable eliminated.

Last updated date: 23rd Sep 2023

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