Solve the given pair of linear equation by the elimination method… - Vidyadip

Question

Solve the given pair of linear equation by the elimination method and the substitution method: $3x + 4y = 10$ and $2x – 2y = 2$

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Answer

By Elimination method,
The given system of equation is :
$3 x + 4 y = 10 ...................(1)$
$2 x - 2 y = 2 ...................(2)$
Multiplying equation$(2)$ by $2,$ we get
$4 x - 4 y = 4 ...................(2)$
Adding equation $(1)$ and equation $(3),$ we get
$7 x = 14$
$\therefore \quad x = \frac { 14 } { 7 } = 2$
Substituting this value of $x$ in equation $(2),$ we get
$2(2) - 2y = 2$
$\Rightarrow \quad 4 - 2 y = 2$
$\Rightarrow \quad 2 y = 4 - 2$
$\Rightarrow \quad 2 y = 2$
$\Rightarrow \quad y =\frac22=1$
So, the solution of the given system of equation is
$x = 2, y = 1$
By Substitution method,
The given system of equation is:
$3 x + 4 y = 10.................(1)$
$2 x - 2 y = 2....................(2)$
From equation$(1)$
$3 x=10-4 y$
$x=\left(\frac{10-4 y}{3}\right)$
Put value of x in equation $(2),$
$2 x-2 y=2$
$2\left(\frac{10-4 y}{3}\right)-2 y=2$
$\frac{2(10-4 y)-2 y(3)}{3}=2$
$20-8 y-6 y=6$
$-14 y=-14$
$y = 1$
Putting value of $y = 1$ in equation $(2)$
$2x - 2 = 2$
$x = 2$
Therefore, $x = 2, y = 1$ is the solution.
Verification: Substituting $x = 2, y = 1,$ we find that both the
equation$(1)$ and $(2)$ are satisfied shown below:
$3 x + 4 y = 3 ( 2 ) + 4 ( 1 ) = 6 + 4 = 10$
$2 x - 2 y = 2 ( 2 ) - 2 ( 1 ) = 4 - 2 = 2$
Hence, the solution is correct.

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