Graph or Algebra? Choosing the Best Way to Solve Simultaneous Equations

Two simultaneous equations describe two lines. Their solution is the point where the lines cross.

When a graph helps

A graph gives a quick visual idea of whether there is one solution, no solution or infinitely many solutions. It also helps you estimate the intersection.

When algebra is better

If the intersection is not on tidy grid coordinates, reading from a graph only gives an approximation. Elimination or substitution gives the exact answer.

Substituting gives: