If either of the variable terms would cancel out the corresponding variable term in the other equation, you can use the Elimination Method to solve the system.
( 1617, 1517)
Practice makes perfect
Since none of the variables are isolated and the y-terms have opposite signs, we will use the Elimination Method. To solve a system of linear equations this way, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other equation.
12 x+4 y=4 & (I) 2 x- y=1 & (II)
Currently, none of the terms in this system will cancel out. Therefore, we need to find a common multiple between two variable like terms in the system. If we multiply (II) by 4, the y-terms will have opposite coefficients.
12 x+4 y=4 & (I) 4(2 x- y)=4*1 & (II)
⇒
12 x+ 4y=4 & (I) 8 x- 4y=4 & (II)
We can see that the y-terms will eliminate each other if we add (I) to (II).
