Question

Solve by Elimination method:-

x + 2y = 5
2x - 3y = -4​

Answer 1

Answer:-

$\bf{x = 1}$

$\bf{y = 2}$

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• Given:-

$x + 2y = 5 \: \: \: \: \: \: \longrightarrow\bf[eqn.1]$

$2x - 3y= -4 \: \: \: \: \: \: \longrightarrow\bf[eqn.2]$

• Method:-

$Elimination \: Method$

• Solution:-

Multiplying [eqn.1] with 2 :-

$\\ 2x + 4y = 10 \: \: \: \: \: \: \longrightarrow\bf[eqn.3]$

Now, Subtracting [eqn.2] from [eqn.1]:-

$\implies{2x + 4y -(2x - 3y) = 10 - (-4)}$

$\implies{2x + 4y - 2x + 3y = 10 + 4}$

$\implies{ 7y = 14}$

$\implies y ={\dfrac{14}{7}}$

$\implies\bf{y = 2}$

Substituting the above value of $\bf{y=2}$ in $\bf[eqn.1]$:-

$\implies{x + 2y = 5}$

$\implies x + 2(2) = 5$

$\implies x + 4 = 5$

$\implies x = 5 - 4$

$\bf\implies{x= 1}$

Hence,

$\bf{x = 1}$

$\bf{y = 2}$

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Answer 2

x + 2y = 5 —eq(1)
2x - 3y = -4 —eq(2)

Now,Multiply eq(1) by 2 we get,
2x + 4y = 10 —eq(3)

Subtracting eq(2) from eq(3),
2x + 4y = 10
2x - 3y = -4
- + +
——————
7y = 14
y = 2
Now, substituting the value of y in eq (1) we get,
x + 2(2) = 5
x + 4 = 5
x = 5 - 4
x = 1
Hence, x=1 and y=2