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How do you solve linear systems by multiplying first

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1 Answer

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.