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.
Best Solution Method: Elimination (using multiplication) Solution: (2, -5)
Practice makes perfect
We are asked to solve the following system of equations.
2x+3y=-11 & (I) -8x-5y=9 & (II)
Since neither equation has a variable with a coefficient of 1, the Substitution Method may not be the easiest. Instead, we will use the Elimination Method. To do that, one of the variable terms needs to be eliminated when one equation is added to or subtracted from the other equation. This means that either the x- or the y-terms must cancel each other out.
2 x+3 y=-11 & (I) -8 x-5 y=9 & (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 Equation (I) by 4, the x-terms will have opposite coefficients.
4(2 x+3 y)=4(-11) -8 x-5 y=9 ⇓ 8x+12 y=-44 -8x-5 y=9We can see that the x-terms will eliminate each other if we add Equation (I) to Equation (II).
