Solving using substitution
Here is our set of equations.
[tex]\left \{ 9x-2y=-21\atop2x+3y=16[/tex]
First, get one of the variables along on one side in both equations.
[tex]\left \{ 9x=-21+2y\atop2x=16-3y[/tex]
Then, get the same value of that variable in both equations.
(You could divide by 9 and 2 in each equation, for instance.
Here I am multiplying by 2 and 9 because it is easier to work with whole numbers.)
[tex]\left \{ 18x=-42+4y\atop18x=144-27y[/tex]
Set the right side of each equation equal to one another.
[tex]-42+4y=144-27y[/tex]
Solve for y.
[tex]4y=186-27y \\ 31y=186 \\ \boxed{y=6}[/tex]
Use this value in one of our equations to find x.
[tex]2x+3y=16 \\ 2x+3(6)=16 \\ 2x+18=16 \\ 2x=-2\\\boxed{x=-1}[/tex]
