In general, "elimination" (or "addition") means to find some way to eliminate a variable. This is customarily done by multiplying one or another equation by some value, and then adding down. For instance:
. . . . .Solve the following by elimination:
. . . . . . .5x - 6y = -3
. . . . . . .2x - 5y = 4
. . . . .The smallest common multiple of 6 and 5 is 30.
. . . . .The smallest common multiple of 5 and 2 is 10.
. . . . .The 10 is smaller. There's no "rule" about this,
. . . . .but smaller numbers are usually easier, so:
. . . . .. . .2[5x - 6y = -3]
. . . . . . .-5[2x - 5y = 4]
. . . . . . . .10x - 12y = -6
. . . . . . .-10x + 25y = -20
. . . . .Add down to get:
. . . . . . .13y = -26
. . . . . . . . .y = -2
. . . . .Then:
. . . . . . .2x - 5(-2) = 4
. . . .. . . . .2x + 10 = 4
. . . . . . . . . .. . .2x = -6
. . . . . . . . . . .. . .x = -3
. . . . .Solution: (x, y) = (-3, -2)
Follow this procedure with your examples.
If you get stuck, please reply showing your work. Thank you.
Eliz.
