Solutions: Infinitely many solutions. Explanation: See solution.
Practice makes perfect
We want to solve the given system of linear equations.
3 x-2 y=1 & (I) 9 x-6 y=3 & (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.
If we multiply Equation (I) by 3, the y-terms will have opposite coefficients.
( 3)(3 x-2 y)=1( 3) 9 x-6 y=3
⇓
9 x- 6y=3 9 x- 6y=3
Notice that both equations are the same. Therefore, there are infinitely many solutions.
