solev it by eliminating x
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Question :- Solve the pair of linear equations by eliminating x
[tex]\sf \: 2x + 3y - 5 = 0 \: \: \: \\ \\ \sf \: 10x - 21y - 1 = 0 \\ \\ [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Given pair of linear equations is
[tex]\sf \: 2x + 3y - 5 = 0 \: \: \: \\ \\ \sf \: 10x - 21y - 1 = 0 \\ \\ [/tex]
can be rewritten as
[tex]\sf \: 2x + 3y = 5 \: \: \: - - - (1) \\ \\ \sf \: 10x - 21y = 1 - - - (2) \\ \\ [/tex]
On multiply equation (1) by 5, we get
[tex]\sf \: 10x + 15y = 25 - - - (3) \\ \\ [/tex]
On Subtracting equation (3) from equation (2), we get
[tex]\sf \: - 36y = - 24 \\ \\ [/tex]
[tex]\sf \: 3y = 2 \\ \\ [/tex]
[tex]\bf\implies \:y = \dfrac{2}{3} \\ \\ [/tex]
On substituting the value of y in equation (1), we get
[tex]\sf \: 2x + 3 \times \dfrac{2}{3} = 5 \\ \\ [/tex]
[tex]\sf \: 2x + 2 = 5 \\ \\ [/tex]
[tex]\sf \: 2x = 5 - 2\\ \\ [/tex]
[tex]\sf \: 2x = 3\\ \\ [/tex]
[tex]\bf\implies \:x = \dfrac{3}{2} \\ \\ [/tex]
We have to solve the given pair of linear equations by elimination method.
Given Equations :
2x + 3y - 5 = 0.
10x - 21y - 1 = 0.
Transferring constants to the right side,
2x + 3y = 5. (1)
10x - 21y = 1. (2)
Multiplying equation (1) by 5, we get,
10x + 15y = 25. (3)
10x - 21y = 1. (4)
Now, we will subtract equation (3) from (4).
=》36y = 24.
=》y = 2/3.
Substituting the value of y in equation (1),
=》2x + 3(2/3) = 5
=》2x + 2 = 5
=》2x = 3
=》x = 3/2.
Hence, Value of x = 3/2 and y = 2/3.