Question

2x +3y = 4 ; 5x + 6y = 7 find the value of x and y by elimination method

Answer 1

$\bold{\underline{\underline{Given \: Equations}}}$

• 2x + 3y = 4
• 5x + 6y = 7

In elimination method, we have to eliminate one variable in order to find the value of x & y.

In the first Equation, if we multiply the whole equation with 2, then :

⟹ $2(2x + 3y = 4)$

⟹ $4x + 6y = 8$

Here, in both the equations, 6y can be eliminated.

Have a look at the attachment.

⟹ $\sf{\red{x=-1}}$

Let us substitute the value of x in equation 2.

⟹ $5x + 6y = 7$

⟹ $5(-1) + 6y = 7$

⟹ $6y = 7 + 5$

⟹ $y=\frac{12}{6}$

⟹ $\sf{\green{y=2}}$

We found both the values of x & y!

____________________

$\bold{\underline{\underline{VerificatioN}}}$

Let us substitute the values of both x & y in equation 1, to verify.

⟹ $2x+3y=4$

⟹ $2(-1) + 3 \times 2 = 4$

⟹ $- 2 + 6 = 4$

$\boxed{4=4}$

$\sf{Hence\:Verified!}$