Question

Solve the following pair of linear equations : x + 2y = 2 and x – 3y = 7.

Answer 1

Answer:

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Answer 2

AnsWer :

x = 4. and y= -1.

Concepts Required :

General equation,

• a1x+b1y+c1 = 0. , a2x + b2y + c2= 0.
• We have two equation, and we compare both equal get it solution.

Method to find it's solution,

• Elimination method.
• Substitution method.
• Cross Multiplication method.

Solution :

Let's try to apply Substitution method,

we have two equation,

$\tt x + 2y = 2. - - -( 1)\\ \tt x - 3y = 7. - - - (2)$

Taking equation 1,

$\begin{aligned} \tt x + 2y & = \tt 2. \\ \tt x &= \tt 2 - 2y - - - (3) \end{aligned}$

Now,

Putting the equation 3 in equation 2 we get,

$\begin{aligned} \tt x - 3y &= \tt 7. \\ \tt 2 - 2y - 3y & = \tt 7. \\ \tt - 5y & = \tt 5. \\ \tt y & = \tt - 1. \end{aligned}$

Now,

Putting the value y in equation 3, we get

$\begin{aligned} \tt x & = \tt 2 - 2y. \\ \tt x &=\tt 2 - 2( - 1) \\ \tt \</p><p>x & = \tt 4.\end{aligned}$

Therefore, the value of x = 4 and y = -1.