Solve the following simultaneous equation:
$
x + y = 8 \\
3x + 4y = 25 \\
$
Last updated date: 21st Mar 2023
•
Total views: 304.8k
•
Views today: 4.83k
Answer
304.8k+ views
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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
