Substitute the expression for that variable into the other equation.
These steps are illustrated here.
When choosing which equation to use for our substitution, there are some things to think about.
Is one of the variables already isolated in one of the equations? If yes, one step is eliminated and you can use the Substitution Method.
Does one of the equations have a variable with a coefficient of 1? If yes, that is going to be the easiest way to solve for an isolated variable.
In which equation is it easier to isolate a variable?
We have been given the following system of equations.
1.2x+y=2 & (I) 1.4y=2.8x+1 & (II)
Notice that y has a coefficient of 1 in Equation (I) and a coefficient of 1.4 in Equation (II).
1.2x+ 1y=2 & (I) 1.4y=2.8x+1 & (II)
To isolate y in Equation (I) we must subtract 1.2x on both sides. In Equation (II) we must divide by 1.4 on both sides.
Equation (I) Equation (II)
1.2x+1y=2 1.4y=2.8x+1
⇓ ⇓
y=2-1.2x y=2x+1/1.4
In this case subtraction is preferred, since the expression resulting from the division will be more time consuming to substitute into the other expression. Therefore we should choose to isolate y in Equation (I).
