Subjects algebra

Linear Substitution 018D08

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1. **Problem:** Solve the system using substitution for part (a): $$\ell_1: y = 3x - 4$$ $$\ell_2: x + y = 8$$ 2. **Formula and method:** Substitution involves replacing one variable in one equation with an expression from the other equation. 3. **Step 1:** From $$\ell_1$$, we have $$y = 3x - 4$$. 4. **Step 2:** Substitute $$y$$ in $$\ell_2$$: $$x + (3x - 4) = 8$$ 5. **Step 3:** Simplify and solve for $$x$$: $$x + 3x - 4 = 8$$ $$4x - 4 = 8$$ $$4x = 12$$ $$x = 3$$ 6. **Step 4:** Substitute $$x = 3$$ back into $$y = 3x - 4$$: $$y = 3(3) - 4 = 9 - 4 = 5$$ 7. **Step 5:** Check the solution in $$\ell_2$$: $$x + y = 3 + 5 = 8$$ which is true. **Final answer:** $$\boxed{(3, 5)}$$