Solving Systems of Linear Equations: 2x + 3y = 9 and -2x

Math Problem Statement

Solve the system of equations: 2x + 3y = 9 and -2x - 5y = -1.

The system of equations presented in the image is:

1. & \quad 2x + 3y = 9 \\ 2. & \quad -2x - 5y = -1 \end{aligned}$$ We will solve this system of equations using either the substitution method or elimination method. ### Step 1: Add the two equations to eliminate $$x$$ $$(2x + 3y) + (-2x - 5y) = 9 + (-1)$$ $$0x - 2y = 8$$ $$-2y = 8 \quad \Rightarrow \quad y = -4$$ ### Step 2: Substitute $$y = -4$$ into the first equation to find $$x$$ $$2x + 3(-4) = 9$$ $$2x - 12 = 9$$ $$2x = 21 \quad \Rightarrow \quad x = \frac{21}{2}$$ ### Solution: $$x = \frac{21}{2}, \quad y = -4$$ Would you like a detailed explanation of any step? Let me know! --- ### Related Questions: 1. How can substitution be used to solve the same system? 2. Can we verify this solution graphically? 3. How do elimination and substitution methods compare for this problem? 4. What happens if the equations represent parallel lines? 5. How would the solution change if we altered the constants? ### Tip: Always double-check your solution by substituting the values of $$x$$ and $$y$$ back into both original equations.

Drop file here or Click Here to upload

Algebra
Systems of Linear Equations

Substitution method
Elimination method

Properties of equality

Grades 9-11

Solve the System of Linear Equations: 2x + y = 3 and -2x + 5y = -9

Solving Systems of Equations by Elimination: x + 3y = 1, 2x − 5y = −3

Solve the System of Equations 5x + 2y = 1 and -3x + 3y = 5 using Elimination Method

Solve System of Linear Equations: -3x + 9y = -2 and x - 3y = 2

Solving System of Linear Equations by Elimination Method