1. **Problem statement:** We are given two linear equations: $$x_1 + kx_2 = c$$ and $$x_1 + lx_2 = d$$ We need to show that if these two equations have the same solution set, then they must be identical, meaning $$k = l$$ and $$c = d$$. 2. **Understanding the problem:** Two linear equations have the same solution set if every solution that satisfies the first equation also satisfies the second, and vice versa. 3. **Step 1: Assume the two equations have the same solution set.** This means for any pair $$(x_1, x_2)$$ that satisfies the first equation, it also satisfies the second: $$x_1 + kx_2 = c \implies x_1 + lx_2 = d$$ 4. **Step 2: Express $$x_1$$ from the first equation:** $$x_1 = c - kx_2$$ 5. **Step 3: Substitute $$x_1$$ into the second equation:** $$c - kx_2 + lx_2 = d$$ 6. **Step 4: Simplify the equation:** $$c + (l - k)x_2 = d$$ 7. **Step 5: Since the two equations have the same solution set, this must hold for all values of $$x_2$$.** The only way for $$c + (l - k)x_2 = d$$ to be true for all $$x_2$$ is if the coefficient of $$x_2$$ is zero and the constant terms are equal: $$l - k = 0 \implies l = k$$ $$c = d$$ 8. **Conclusion:** If the two linear equations have the same solution set, then $$k = l$$ and $$c = d$$, meaning the two equations are identical. **Final answer:** $$k = l$$ and $$c = d$$.