Question

What is the first step to take when solving this linear system of equations by the addition-subtraction method? 2x + 4y = 3 x + 3y =13

Answer 1

Hey!

2x + 4y = 3x + 3y = 13

2x + 4y = 13 ------------ ( 1 )

3x + 3y = 13 -------------- ( 2 )

Now, we will need to eliminate one type of the term , let us eliminate the x terms

Let us multiply the first equation with 3 and the second equation with 2

3 ( 2x + 4y ) = 3 ( 13 )

2 ( 3x + 3y ) = 2 ( 13 )

................................................................................................................................................

6x + 12y = 39 ----------------- ( 1 )

6x + 6y = 26 ---------------------- ( 2 )

Now, let us subtract the second equation from the first equation

6x + 12y = 39

-6x - 6y = - 26

.........................................

6y = 13

y = 13 / 6

...........................................

Now substitute the value of ' y ' and we can get the value of ' x '

I will take 3x + 3y = 13

3x + ( 3 ) ( 13 / 6 ) = 13

3x + 13 / 2 = 13

3x = 13 - 13/2

LCM = 2

3x = 26 - 13 / 2

3x = 13 / 2

x = 13/2 / 3

x = 13/2 × 1/3

x = 13/6

Hope my answer helps!