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

Math Problem Statement

-x - y = -3, -2x - 3y = -7

Let's solve the system of equations from the image step by step:

The system of equations is:

1. \ -x - y &= -3 \\ 2. \ -2x - 3y &= -7 \end{aligned}$$ ### Step 1: Solve the first equation for $$y$$ Starting with equation 1: $$-x - y = -3$$ Solve for $$y$$: $$y = -x + 3$$ ### Step 2: Substitute $$y$$ into the second equation Now substitute $$y = -x + 3$$ into equation 2: $$-2x - 3(-x + 3) = -7$$ Simplify: $$-2x + 3x - 9 = -7$$ Combine like terms: $$x - 9 = -7$$ Add 9 to both sides: $$x = 2$$ ### Step 3: Substitute $$x = 2$$ back into the first equation to find $$y$$ Now, substitute $$x = 2$$ into the expression for $$y$$: $$y = -2 + 3 = 1$$ ### Final Answer The solution is $$(x, y) = (2, 1)$$. Would you like further clarification or details on any of the steps? Here are 5 related questions you might find useful: 1. How can you graphically represent this system of equations? 2. How do you solve systems of equations using substitution in general? 3. What are the other methods to solve systems of linear equations (e.g., elimination)? 4. What happens if a system of equations has no solutions or infinite solutions? 5. How do you apply systems of equations in real-life scenarios? **Tip:** Always double-check your substitutions to ensure accuracy when solving systems of equations.

Drop file here or Click Here to upload

Algebra
Linear Equations
Systems of Equations

Substitution method: Solve one equation for a variable and substitute it into the other equation

None

Grades 8-10

Solve the System of Equations Using Substitution

Solving the System of Equations 2x - y = 7 and x + 3y = -7 to Find 3x - 4y

Solve System of Equations Using Substitution Method: 2x+3y = -7, 2x-y = 1

Solve the System of Equations Using Substitution: -2x + 5y = 7 and y = -3x - 2

Solve System of Linear Equations: 3x + 2y = 7 and x - y = -1