Solving Systems of Linear Equations with Substitution

Solve the system:
x + 6y = 17
x - 3y = 8

• (5, 2)

• (11, 1)

• (1, 11)

• no solution

What does
"solution to a system of equations"
mean?

• It's the point where both equations equal zero

• It's the point where graphs of both equations cross the y-axis

• It's the point that solves both equations at the same time

• It's the point where graphs of both equations cross the x-axis

When solving a system of equations algebraically, which statement results in infinite solutions?

• 4 = 7

• 2 = 2

• -3 = 3

• all of the above

a method of solving a system of equations by taking a variable out and replacing it with an expression.

• Systems by Graphing

• Systems by Substitution

• Systems by Elimination

• Systems by Drawing

2 or more linear equations with the same set of variables

• System

• System of Equations

• Linear Equations

• Quadratic Equations

a solution to a system that results in one x value and one y value that will satisfy both equations 

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

a solution to a system that results in an unlimited amount of x values and an unlimited amount of y values that will satisfy both equations

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

a solution to a system of equations that results in no x or y value that will satisfy both equations

• No Solution

• One Solution

• Infinite Solutions

• Beyond Solutions

What is the solution to this system of equations? Solve by substitution or graphing.

• (7, -8)

• (-7, 8)

• (-7, -8)

• (7, 8)

Solve the system by substitution.

−x + 5y = 12

y = −2x − 2

• (−2, −7)

• (−2, 2)

• (−2, −2)

• (2, −2)