Question

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

(2x−3y=−6) (x+3y=12)
What is the solution? Write the ordered pair using integers or fractions.

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