Explain how to determine that a given ordered pair is a solution of a system of equations.
Determine whether \left(5, 2\right) is a solution of the given system of equations:
Determine whether \left(4, 17\right) is a solution of the given system of equations:
Determine whether the following points are solutions of the given system of equations:
\left(2, 5\right)
\left(3, 4\right)
Determine whether the following points are solutions of the given system of equations:
\left(5, 3\right)
\left(7, 13\right)
Determine whether the following points are solutions of the given system of equations:
\left(5, -1\right)
\left(4, 3\right)
Determine whether the following points are solutions of the given system of equations:
\left(4, 16\right)
\left(2, 18\right)
Describe the graphical solution of a system of two linear equations.
Consider a system consisting of two straight lines with different gradients. How many points of intersection will the lines have?
The following graph displays a system of two equations:
State the solution to the system in the form \left(x, y\right).
For each of the following pairs of linear equations:
Sketch the lines of the two equations on the same number plane.
Hence, state the values of x and y which satisfy both equations.
y = x + 0 and y = - 1
y = \dfrac {x}{3} + \dfrac {1}{3} and - 8 y = 8 x + 8
y = 2 x + 2 and y = - 2 x + 2
How many solutions does the given system of equations have? Explain your answer.
Consider the following system of equations:
For which value of b does the system have an infinite number of solutions?
For which values of b does the system have no solutions?
Solve the following pairs of simultaneous equations using the substitution method:
y=-5x - 23 \\ y = 7x + 25
y=5x+34 \\ y=3x+18
\begin{aligned} y &= -4x - 17 \\ 3y &= 21x + 147 \end{aligned}
\begin{aligned} y &= -6 x - 26 \\ x + y &= -6 \end{aligned}
\begin{aligned} y &= 3 x - 18 \\ x - y &= 10 \end{aligned}
\begin{aligned} y &= -5 x + 22 \\ 6 x + y &= 26\end{aligned}
\begin{aligned} y &= 6 x - 2 \\ -3 x - y &= -7 \end{aligned}
\begin{aligned} y &= 8 x - 30 \\ 5 x + 9 y &= 38 \end{aligned}
\begin{aligned} y &= -2 x - 1 \\ x + 2 y &= 13 \end{aligned}
\begin{aligned} 4 x + 3 y &= 52 \\ 7 x - 5 y &= 9 \end{aligned}
\begin{aligned} x &= -5y - 27 \\ x &= 7y + 45 \end{aligned}
\begin{aligned} x &= -4 y - 39 \\ 4 x &= 24 y + 164 \end{aligned}
\begin{aligned} x &= 4 y - 27 \\ 2 y + x &= 21 \end{aligned}
\begin{aligned} x &= 3 y - 21 \\ 8 y + 5 x &= 79 \end{aligned}
\begin{aligned} 3 y + 2 x &= 37 \\ 9 y - 5 x &= 56 \end{aligned}
Consider the following system of linear equations:
\begin{aligned} y &= x + 8 \\ y &= - 7 x + 16 \end{aligned}Use the substitution method to solve the system of equations.
Use the elimination method to solve the system of equations.
Do both methods give the same solution?
Consider the given system of equations:
Equation 1: 3x - 7y = 4
Equation 2: -12x + 28y = -16
Rearrange Equation 1 to find x in terms of y.
Substitute your expression for x into Equation 2 and solve for the value of y.
State whether the system of equations is inconsistent, dependent or independent.
Solve the following pairs of simultaneous equations using the elimination method:
Solve the following pairs of simultaneous equations using an appropriate algebraic method:
\begin{aligned} x + y &= 8 \\ 2x - 3y &= 26 \end{aligned}
\begin{aligned} y &= 2x + 16 \\ y &= 3x + 21 \end{aligned}
\begin{aligned} y &= 4x - 17 \\ x + y &= 38 \end{aligned}
\begin{aligned} 3x + y &= 22 \\ y &= -2x + 10 \end{aligned}
\begin{aligned} 2x + y &= 5 \\ 5x + 3y &= 9 \end{aligned}
\begin{aligned} 11x + 6y &= 27 \\ 7x + 6y &= -9 \end{aligned}
\begin{aligned} 6x + 10y &= 59 \\ -4x + 5y &= 19 \end{aligned}
\begin{aligned} 18x - 7y &= -64 \\ 3x + 5y &= 14 \end{aligned}
\begin{aligned} 5x - 3y &= 46 \\ 3x + 10y &= 4 \end{aligned}
\begin{aligned} \dfrac{x}{2} + 3y &= -6 \\ - \dfrac{x}{4} + y &= -7 \end{aligned}
Solve the following pairs of equations by using your CAS calculator, or other technology, to graph the lines on the same number plane:
Graph the following lines on the same set of axes on your CAS calculator, or other technology, to determine how many solutions there are to the system of equations:
\begin{aligned} 6x - y &= 1 \\ 12x - 2y &= 2 \end{aligned}Consider the following equations:
Equation 1: x - y = - 6
Equation 2: - x + 2 y = 9
Equation 3: 2 x - 7 y = - 42
Graph the following pairs of equations using technology, and state the solution to each system of equations:
Equations 1 and 2
Equations 1 and 3
Equations 2 and 3
Solve each of the following systems of linear equations using the solving functionality of your CAS calculator:
y = 4 x + 35 \\ y = 2 x + 21
y = 2.7 x - 17.41 \\ y = - 9.8 x + 13.84
\dfrac {1}{3} x + \dfrac {2}{3} y = 1
\dfrac {1}{2} x + \dfrac {1}{3} y = 7