How do you solve linear systems by multiplying first

Question

I don't understand how to do this and I am very confused.

Answer 1

4x+6y=12

3x+5y=18

 

If you want to solve the linear system by multiplying, pick a variable to eliminate.  If you choose the x, multiply the line by the x coefficient of the other line.

 

3(4x+6y=12)
4(3x+5y=18)

 

Distribute the factor to each term.

 

12x+18y=36

12x+20y=72

 

Subtract each term from the line above

 

   12x+18y=36

 -(12x+20y=72)

   0    -  2y =-36

 

Solve for y.

 

y=18

 

Plug the value for y into one of the original equations and solve for x.

 

3x+5(18)=18

3x+90=18

3x=-72

x=-24

 

(-24,18) works for both equations.

 

There are variations to the method I used, but the solution will stay the same.