1. **State the problem:** Solve the system of equations: $$X + m - t = 150$$ $$X - m + t = 110$$ 2. **Formula and rules:** To solve a system of linear equations, we can use addition or subtraction to eliminate one variable. 3. **Add the two equations:** $$ (X + m - t) + (X - m + t) = 150 + 110 $$ Simplify: $$ X + m - t + X - m + t = 260 $$ $$ 2X = 260 $$ 4. **Solve for $X$:** $$ X = \frac{260}{2} = 130 $$ 5. **Substitute $X=130$ into the first equation:** $$ 130 + m - t = 150 $$ Simplify: $$ m - t = 20 $$ 6. **Substitute $X=130$ into the second equation:** $$ 130 - m + t = 110 $$ Simplify: $$ -m + t = -20 $$ 7. **Rewrite the two equations for $m$ and $t$:** $$ m - t = 20 $$ $$ -m + t = -20 $$ 8. **Add these two equations:** $$ (m - t) + (-m + t) = 20 + (-20) $$ Simplify: $$ 0 = 0 $$ This means the two equations are dependent and represent the same line. 9. **Express $m$ in terms of $t$:** From $m - t = 20$, we get: $$ m = t + 20 $$ **Final answer:** $$ X = 130 $$ $$ m = t + 20 $$ where $t$ is any real number.