Math Problem Statement

What is the solution to the system of linear equations? 2x - 3y = -1 and y = x - 1

Solution

The given system of linear equations is:

2x3y=12x - 3y = -1 y=x1y = x - 1

To solve this, we can substitute the second equation y=x1y = x - 1 into the first equation:

  1. Substitute y=x1y = x - 1 into 2x3y=12x - 3y = -1: 2x3(x1)=12x - 3(x - 1) = -1

  2. Simplify the equation: 2x3x+3=12x - 3x + 3 = -1

  3. Combine like terms: x+3=1-x + 3 = -1

  4. Solve for xx: x=13-x = -1 - 3 x=4x=4-x = -4 \quad \Rightarrow \quad x = 4

  5. Now, substitute x=4x = 4 into the second equation y=x1y = x - 1: y=41=3y = 4 - 1 = 3

So, the solution is (x,y)=(4,3)(x, y) = (4, 3).

The correct answer from the given choices is (4, 3).

Would you like more details or have any other questions?

Here are five related questions:

  1. How do you solve a system of equations using substitution in general?
  2. What is the method of elimination, and how is it different from substitution?
  3. How can you check if your solution to a system of linear equations is correct?
  4. Can a system of linear equations have no solution or infinitely many solutions?
  5. What is the graphical interpretation of solving a system of two linear equations?

Tip: Substitution is often useful when one equation is already solved for a variable, as it simplifies the process.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

Substitution Method
Solving Linear Systems

Theorems

None

Suitable Grade Level

Grades 8-10