Describe the graphical solution of a system of two linear equations.
Each graph below shows a system of two equations. Write down the solution to each system as a point in the form \left(x, y\right).
The following graph displays a system of two equations.
The following graph displays a system of two equations.
How many solutions does this system of equations have?
Explain how to determine that a given ordered pair is a solution of a system of equations.
Consider the system of equations:
\begin{aligned} y &= x + 4 \\ y &= 2 x + 1 \end{aligned}
Is \left(3, 7\right) a solution of the system of equations?
Is \left(2, 6\right) a solution of the system of equations?
Consider the system of equations:
\begin{aligned} y &= x - 8 \\ y &= -2x + 1 \end{aligned}
Is \left(3, -5\right) a solution of the system of equations?
Is \left(6, -2\right) a solution of the system of equations?
Consider the system of equations:
\begin{aligned} y &= x + 8 \\ y &= 3x + 2 \end{aligned}
Is \left(3, 11\right) a solution of the system of equations?
Is \left(2, 10\right) a solution of the system of equations?
Determine whether each ordered pair is a solution of the system of linear equations:
\begin{aligned} x + y &= 10 \\ 2 x + 6 y &= 48 \end{aligned}
\left(1, 9\right)
\left(3, 7\right)
Determine whether each ordered pair is a solution of the system of linear equations:
\begin{aligned} x + y &= 10 \\ 2x + 6y &= 48 \end{aligned}
\left(4, 6\right)
\left(3, 7\right)
Determine whether each ordered pair is a solution of the system of linear equations:
\begin{aligned} 4 y &= 5 x - 13 \\ 5 x - y &= 22 \end{aligned}
\left(5, 3\right)
\left(7, 13\right)
Determine whether each ordered pair is a solution of the system of linear equations:
\begin{aligned} 4 x &= 19 - y \\ x - 3 y &= - 5 \end{aligned}
\left(5, -1\right)
\left(4, 3\right)
Determine whether each ordered pair is a solution of the system of linear equations:
\begin{aligned} 5y &= 3x + 11 \\ 5x - y &= 11 \end{aligned}
\left(3, 4\right)
\left(5, 14\right)
Consider the system of linear equations:
\begin{aligned} 5x &= 28 - y \\ x - 4y &= -7 \end{aligned}
Determine if the following points solve the equations simultaneously:
\left(3, 16\right)
\left(5, 3\right)
Consider the system of equations:
\begin{aligned} y &= x - 8 \\ y &= - 2 x + 1 \end{aligned}
Determine if the following points satisfy the system:
\left(3, - 5 \right)
\left(6, - 2 \right)
\left(4, - 4 \right)
Consider the system of equations:
\begin{aligned} y &= x - 11 \\ y &= -3x + 1 \end{aligned}
Determine if the following points satisfy the system:
\left(3, -8\right)
\left(4, -7\right)
\left(6, -5\right)
Consider the system of equations:
\begin{aligned} y &= x - 8 \\ y &= -3x + 4 \end{aligned}
Determine if the following points satisfy the system:
\left(3, -5\right)
\left(4, -4\right)
\left(5, -3\right)
Determine whether each ordered pair is a solution of the system of linear equations:
\begin{aligned} y &= 5x - 4 \\ y &= -x + 20 \end{aligned}
\left(4, 16\right)
\left(2, 18\right)
\left(3, -11\right)
Determine whether each ordered pair is a solution of the system of linear equations:
\begin{aligned} x + 4 y &= 10 \\ x - y &= - 5 \end{aligned}
\left(3, 2\right)
\left(2, 2\right)
\left( - 2 , 3\right)
Determine if following ordered pairs is a solution to the system of equations:
\begin{aligned} y &= 2x - 3 \\ y &= -x + 3 \end{aligned}
\left(4, -1\right)
\left(3, -3\right)
\left(2, 1\right)
Determine if following ordered pairs is a solution to the system of equations:
\begin{aligned} x + 4y &= 14 \\ x - y &= -6 \end{aligned}
\left(3, 3\right)
\left(2, 3\right)
\left(-2, 4\right)
Does there exist a value for x and y that satisfy the following two equations simultaneously?
Consider the following system of equations:
\begin{aligned} x + y &= 7 \\ x - y &= 3 \end{aligned}
Using the first equation, x + y = 7, find the value of y when x = 5.
Using the second equation, x - y = 3, find the value of y when x = 5.
Is \left(5, 2\right) a solution of the system?
Consider the following system of equations:
\begin {aligned} 2 x + 7 y &= - 13 \\ 3 x + 8 y &= - 4 \end{aligned}
Using the first equation, 2 x + 7 y = - 13, find the value of y when x = 4.
Using the second equation, 3 x + 8 y = - 4, find the value of y when x = 4.
Is \left(4, - 3 \right) a solution of the system?
Consider the following system of equations:
\begin{aligned} y &= 6 x - 7 \\ 4 x + 3 y &= 67 \end{aligned}
Using the first equation, y = 6 x - 7, find the value of y when x = 4.
Using the second equation, 4 x + 3 y = 67, find the value of y when x = 4.
Is \left(4, 17\right) a solution of the system?
Consider the following system of equations:
\begin{aligned} x + y &= 9 \\ x - y &= -5 \end{aligned}
Consider the following system of equations:
\begin{aligned} y &= 2x - 9 \\ 4x + 3y &= 3 \end{aligned}
Using the first equation, y = 2x - 9, find the value of y when x = 3.
Using the second equation, 4x + 3y = 3, find the value of y when x = 3.
Is \left(3, -3\right) a solution of the system?
Find the coordinates of the point of intersection for the following pairs of lines:
The vertical line x = 2 meets the line y = 7 x-1.
The vertical line x = 2 meets the line y = 7x - 2.
The horizontal line y = 3 meets the line y = 2 x - 3.
The horizontal line y = -4 meets the line y = 4x + 4.
Consider a system consisting of two straight lines with different gradients.
Which of the following statement is true?
If two lines have different gradients, then they must intersect.
Even if two lines have different gradients, they still might not intersect.
How many solutions will our system of two straight lines have?