Solving System of Equations Using Substitution: -x + y = -1, 4x

Math Problem Statement

solve

Use the substitution method to solve the system: -x + y = -1, 4x - 3y = 3

We are given a system of equations and asked to solve it using the substitution method. The system is:

-x + y = -1 \\ 4x - 3y = 3 \end{cases}$$ ### Step 1: Solve one equation for one variable We can solve the first equation for $$y$$: $$-x + y = -1 \implies y = x - 1$$ ### Step 2: Substitute the expression for $$y$$ into the second equation Now substitute $$y = x - 1$$ into the second equation $$4x - 3y = 3$$: $$4x - 3(x - 1) = 3$$ Simplify: $$4x - 3x + 3 = 3$$ $$x + 3 = 3$$ $$x = 0$$ ### Step 3: Solve for $$y$$ Now that we know $$x = 0$$, substitute this back into the equation for $$y$$: $$y = x - 1 = 0 - 1 = -1$$ ### Final Solution: The solution to the system is $$x = 0$$ and $$y = -1$$. Thus, the solution is: $$(0, -1)$$ Would you like further details or have any questions? Here are 5 related questions to consider: 1. How do you apply the substitution method in different systems of equations? 2. What happens if both equations represent the same line? 3. How can you check if a system has no solution or infinite solutions? 4. What are the differences between substitution and elimination methods? 5. Can all systems of equations be solved using the substitution method? **Tip:** Always check your solution by substituting the values back into the original system of equations to verify.

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Algebra
System of Linear Equations
Substitution Method

-x + y = -1
4x - 3y = 3

Linear System Solving Methods

Grades 8-10

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