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