Math Problem Statement

give me questions for solve each system of linear equations by subsitution

Solution

Here are five practice questions for solving systems of linear equations by substitution:

  1. Solve the system of equations: x+y=5x + y = 5 2xy=42x - y = 4

  2. Solve the system of equations: 3x+4y=123x + 4y = 12 xy=1x - y = 1

  3. Solve the system of equations: x=2y+3x = 2y + 3 4xy=104x - y = 10

  4. Solve the system of equations: 5x+2y=145x + 2y = 14 2xy=32x - y = 3

  5. Solve the system of equations: x=3y1x = 3y - 1 2x+4y=102x + 4y = 10

Would you like to see the solutions or need clarification on any of these?


Here are some follow-up questions you might find interesting:

  1. How do you check the solution of a system of equations after solving it?
  2. What happens if a system has no solution or infinite solutions?
  3. How do you solve a system using the elimination method as an alternative to substitution?
  4. Can substitution work with non-linear systems of equations?
  5. What is the graphical interpretation of the solution to a system of linear equations?

Tip: Always solve for one variable first and then substitute it into the other equation to avoid dealing with complex expressions right away.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Substitution Method

Formulas

Substitution method: Solve for one variable in terms of the other, then substitute into the second equation
General form of a linear equation: ax + by = c

Theorems

Substitution Theorem: If two expressions are equal, one can be substituted for the other in an equation

Suitable Grade Level

Grades 8-10