A system of equations is solved by eliminating variables step by step to reveal consistent values.

Solve:

\[ 2x+3y=13 \] \[ x-y=1 \]

Solution:

\[ \text{Rewrite the second equation:} \] \[ x=y+1 \] \[ \text{Substitute into the first equation:} \] \[ 2(y+1)+3y=13 \] \[ \text{Expand brackets:} \] \[ 2y+2+3y=13 \] \[ \text{Combine like terms:} \] \[ 5y+2=13 \] \[ \text{Subtract 2:} \] \[ 5y=11 \] \[ \text{Divide by 5:} \] \[ y=\frac{11}{5} \] \[ \text{Substitute back to find } x: \] \[ x=\frac{11}{5}+1=\frac{16}{5} \]

Final Answer:

Triangle Area Geometry Worked Example Triangle Area Geometry Worked Example
Algebraic Equation Solved Step by Step Algebraic Equation Solved Step by Step

\[ x=\frac{16}{5},\quad y=\frac{11}{5} \]

Elimination reveals both variables clearly.