Solving Systems of Linear Equations (2024)

What is a system of linear equations?

Which of the following methods is used to solve systems of linear equations?

What is the slope-intercept form of a linear equation?

What is the purpose of the slope-intercept form of a linear equation?

What is the standard form of a linear equation?

What is the purpose of the standard form of a linear equation?

How can the standard form of a linear equation be converted to slope-intercept form?

What is the first step in the substitution method for solving systems of linear equations?

What is the final step in the elimination method for solving systems of linear equations?

Solving Systems Of Equations

• A system of linear equations is a set of two or more linear equations that must be true at the same time.
• Systems of equations can be solved using:
  • Substitution method
    • Elimination method
  • Graphical method

Substitution Method

• Solve one equation for one variable
• Substitute the expression into the other equation
• Solve for the other variable
• Substitute the value of the variable back into one of the original equations to find the value of the other variable

Elimination Method

• Make the coefficients of one variable opposites
• Add the equations to eliminate the variable
• Solve for the remaining variable
• Substitute the value of the variable back into one of the original equations to find the value of the other variable

Slope-Intercept Form

• The slope-intercept form of a linear equation is given by:
  • y = mx + b
  • m is the slope (rate of change)
  • b is the y-intercept (point where the line crosses the y-axis)
• Slope-intercept form is useful for:
  • Graphing linear equations
  • Identifying the slope and y-intercept of a line

Standard Form

• The standard form of a linear equation is given by:
  • Ax + By = C
  • A, B, and C are integers
  • A and B are not both zero
• Standard form is useful for:
  • Writing linear equations in a consistent format
  • Solving systems of linear equations
• Standard form can be converted to slope-intercept form by:
  • Rearranging the equation to isolate y
  • Dividing by the coefficient of y (if necessary)

Systems of Linear Equations

• A system consists of two or more linear equations that must be true at the same time
• Can be solved using three methods: Substitution, Elimination, and Graphical method

Solving Systems of Equations using Substitution Method

• Solve one equation for one variable
• Substitute the expression into the other equation to solve for the other variable
• Substitute the value of the variable back into one of the original equations to find the value of the other variable

Solving Systems of Equations using Elimination Method

• Make the coefficients of one variable opposites
• Add the equations to eliminate the variable
• Solve for the remaining variable
• Substitute the value of the variable back into one of the original equations to find the value of the other variable

Slope-Intercept Form

• Equation is given by: y = mx + b
• m represents the slope (rate of change)
• b represents the y-intercept (point where the line crosses the y-axis)
• Useful for graphing linear equations and identifying the slope and y-intercept of a line

Standard Form

• Equation is given by: Ax + By = C
• A, B, and C are integers
• A and B are not both zero
• Useful for writing linear equations in a consistent format and solving systems of linear equations
• Can be converted to slope-intercept form by rearranging the equation to isolate y and dividing by the coefficient of y (if necessary)

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