Question

What is the correct first step to solve this system of equations by elimination?

Answer 1

$\bold{\huge{\pink{\underline{ Solution }}}}$

$\bold{\underline{ Given }}$

• We have given two linear equations that is 2x - 3y = -6 and x + 3y = 12 .

$\bold{\underline{ To \: Find }}$

• We have to find the value of x and y by elimination method.

$\bold{\underline{ Let's \: Begin }}$

$\sf{ 2x - 3y = -6 ...eq(1)}$

$\sf{ x + 3y = 12 ...eq(2)}$

Multiply eq( 2 ) by 2 :-

$\sf{ 2( x + 3y = 12 )}$

$\sf{ 2x + 6y = 24 }$

Subtract eq(1) from eq(2) :-

$\sf{ 2x + 6y -( 2x - 3y) = 24 -(-6)}$

$\sf{ 2x + 6y - 2x + 3y = 24 + 6 }$

$\sf{ 9y = 30 }$

$\sf{ y = 30/9}$

$\sf{\red{ y = 10/3}}$

Now, Subsitute the value of y in eq( 1 ):-

$\sf{ 2x - 3(10/3) = -6 }$

$\sf{ 2x - 10 = -6 }$

$\sf{ 2x = -6 + 10}$

$\sf{ x = 4/2}$

$\sf{\red{ x = 2}}$

Hence, The value of x and y is 2 and 10/3