Solve a System of Linear Equations Using Substitution

Math Problem Statement

Solve

Use the substitution method to find all solutions of the system of equations: x - y = 1 4x + 3y = 25

We are tasked with solving a system of equations using the substitution method. The given system is:

1. & \quad x - y = 1 \\ 2. & \quad 4x + 3y = 25 \end{aligned}$$ ### Step-by-Step Solution: 1. **Solve the first equation for $$x$$:** $$x - y = 1 \quad \Rightarrow \quad x = y + 1$$ 2. **Substitute this expression for $$x$$ into the second equation:** $$4(y + 1) + 3y = 25$$ 3. **Expand and simplify:** $$4y + 4 + 3y = 25 \quad \Rightarrow \quad 7y + 4 = 25$$ 4. **Solve for $$y$$:** $$7y = 25 - 4 \quad \Rightarrow \quad 7y = 21 \quad \Rightarrow \quad y = \frac{21}{7} = 3$$ 5. **Substitute $$y = 3$$ back into the expression for $$x$$:** $$x = y + 1 = 3 + 1 = 4$$ ### Final Solution: $$(x, y) = (4, 3)$$ Do you need further details or have any questions? ### Related Questions: 1. Can this system of equations be solved using the elimination method? 2. How can we verify the solution of a system of equations? 3. What are the differences between the substitution and elimination methods? 4. Can this system be solved graphically, and how would the graph look? 5. What is the general approach to solving nonlinear systems using substitution? ### Tip: Always verify your solutions by substituting the values back into the original system to ensure they satisfy both equations.

Drop file here or Click Here to upload

Algebra
Linear Equations
Substitution Method

x = y + 1
4(y + 1) + 3y = 25

Substitution Method for Solving Systems of Linear Equations

Grades 8-10

Solving Systems of Linear Equations using Substitution Method

Solving Systems of Linear Equations for y = 25 + 30x and y = 15 + 32x

Solving a System of Equations Using the Substitution Method

Solving Linear Equations with Substitution Method: 4x - 8y = 11, x + 5y = 1

Solve the System of Equations: 7x - 3y = -25, 4x + 5 = y