Solve the System of Equations x + 2y + 1 = 0 and 2x - 3y

Math Problem Statement

Solve the system of equations: x + 2y + 1 = 0 and 2x - 3y - 12 = 0 using substitution or elimination methods.

The image contains several systems of equations to solve using substitution and elimination methods. Let's work on one of them.

1.\quad & x + 2y + 1 = 0 \quad & (i) \\ & 2x - 3y - 12 = 0 \quad & (ii) \end{aligned}$$ **Step 1: Solve one equation for one variable (using substitution).** From equation (i): $$x + 2y + 1 = 0 \quad \Rightarrow \quad x = -2y - 1 \quad \text{(iii)}$$ **Step 2: Substitute this expression for $$x$$ into equation (ii).** Substitute $$x = -2y - 1$$ into equation (ii): $$2(-2y - 1) - 3y - 12 = 0$$ Simplifying: $$-4y - 2 - 3y - 12 = 0$$ $$-7y - 14 = 0 \quad \Rightarrow \quad y = -2$$ **Step 3: Substitute $$y = -2$$ back into equation (iii) to find $$x$$.** $$x = -2(-2) - 1 = 4 - 1 = 3$$ Thus, the solution is $$x = 3$$ and $$y = -2$$. Would you like a solution for any other problem from the image? ### 5 related questions: 1. Can you solve another system of equations from this image using elimination instead? 2. How does substitution compare to elimination in terms of solving speed for larger systems? 3. How do you graphically represent the solution of a system of linear equations? 4. What happens if two lines in a system of equations are parallel? 5. How can we solve a system where both equations are quadratic? ### Tip: Always check your solutions by substituting both variables back into the original equations to confirm the results.

Drop file here or Click Here to upload

Algebra
Systems of Linear Equations

Substitution method
Elimination method

System of Linear Equations Theorem

Grades 8-10

Solve System of Linear Equations: 3x + 2y = -3 and 18x + 2y = 12

Solve System of Equations by Elimination - Step-by-Step Solution

Solving a System of Linear Equations: 3x + 2y = 12 and x - y = -12

Solve the System of Linear Equations: x + 2y = 12, 3x - 5y = 3

Solving System of Linear Equations 2x + 3y = 12 and x - y = 1