Solving a System of Linear Equations Using the Addition Method

Math Problem Statement

Solve the system by the addition method: x + y = -7 and x - y = -3

The problem asks to solve the system of linear equations using the addition method:

x + y &= -7 \\ x - y &= -3 \end{aligned}$$ ### Step 1: Add the two equations. When we add the two equations, the $$y$$'s will cancel out: $$(x + y) + (x - y) = -7 + (-3)$$ This simplifies to: $$2x = -10$$ ### Step 2: Solve for $$x$$. $$x = \frac{-10}{2} = -5$$ ### Step 3: Substitute $$x = -5$$ into one of the original equations. Substitute into the first equation $$x + y = -7$$: $$-5 + y = -7$$ ### Step 4: Solve for $$y$$. $$y = -7 + 5 = -2$$ ### Final Solution: The solution set is $$(-5, -2)$$. Thus, the correct choice for this problem is: $$\boxed{(-5, -2)}$$ Would you like further details or have any questions? Here are 5 related questions that build on this: 1. How do you solve a system of equations using substitution? 2. What are the conditions for a system of equations to have infinitely many solutions? 3. How do you recognize a system of equations with no solution? 4. What is the graphical interpretation of solving a system of two equations? 5. How can the elimination method be used for systems of equations with three variables? **Tip:** When solving systems of equations using the addition (elimination) method, always aim to eliminate one variable by adding or subtracting the equations, making sure that the coefficients of that variable are opposites.

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Algebra
Linear Equations
System of Equations
Addition (Elimination) Method

Addition of equations: (x + y) + (x - y)
Solution for x: x = (-sum of constants) / 2

Addition (Elimination) Method for solving systems of linear equations

Grades 9-11

Solve a Linear System using Elimination: -x - y = -6 and -7x - y = -30

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Solve the System of Equations: x + y = 3, x + 2y = -1 using Elimination

Solving a System of Linear Equations: -x - y = -3 and -2x - 3y = -7

Solving Systems of Equations Using Elimination: 4x + y = 7, -5x - y = -10