Solve System of Linear Equations by Substitution: -y = x, -7x

Math Problem Statement

Solve the system by substitution: -y = x, -7x - 5y = -20.

To solve the system of equations by substitution given in the image:

1. & \quad -y = x \quad \text{(Equation 1)} \\ 2. & \quad -7x - 5y = -20 \quad \text{(Equation 2)} \end{aligned}$$ ### Step 1: Solve Equation 1 for $$y$$ From Equation 1: $$y = -x$$ ### Step 2: Substitute $$y = -x$$ into Equation 2 Substitute $$y = -x$$ into Equation 2: $$-7x - 5(-x) = -20$$ Simplify the equation: $$-7x + 5x = -20$$ $$-2x = -20$$ Solve for $$x$$: $$x = 10$$ ### Step 3: Substitute $$x = 10$$ back into Equation 1 Now substitute $$x = 10$$ back into $$y = -x$$ to find $$y$$: $$y = -10$$ ### Solution The solution to the system of equations is: $$\boxed{(10, -10)}$$ Would you like any further details or have any questions? --- Here are 5 related questions to expand your understanding: 1. How can you verify the solution to a system of linear equations? 2. What are some alternative methods to solve a system of equations besides substitution? 3. What is the significance of the slope in the linear equations when solving graphically? 4. How do systems of equations behave when they have no solutions or infinitely many solutions? 5. Can you solve a system of equations if one or both are non-linear? **Tip:** Always check your solution by substituting the values back into the original equations. This ensures that your answer is correct!

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Algebra
Linear Equations
Substitution Method

Substitution method in solving systems of equations

Basic properties of equality and linear equations

Grades 8-10

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