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).
Consider the graph showing a system of two equations:
How many solutions does this system of equations have?
Write down the solution to the system of equations as an ordered pair \left(x, y\right).
Consider the graph showing a system of two equations:
How many solutions does this system of equations have?
Consider the graph of the equation \\y = 5 x + 3:
If a second line y = mx + b intersects this line at the point \left(0, 3\right), state the value of b.
Consider the following systems of linear equations:
Find the x and y-intercepts of the first equation.
Find the x and y-intercepts of the second equation.
Graph the two equations on the same set of axes.
State the coordinate pair \left(x, y\right) that satisfies both equations.
Consider the following linear equations:
\begin{aligned} y &= 2 x + 2 \\ y &= - 2 x + 2 \end{aligned}
Determine the gradient and y-intercept of the line y = 2 x + 2.
Determine the x\text{ and }y-intercepts of the line y = - 2 x + 2.
Hence sketch the graphs on the same coordinate plane.
State the values of x and y which satisfy both equations.
Consider the following system of equations:
\begin{aligned} y &= 4 x - 3 \\ y &= 4 - 3 x \end{aligned}
Complete the table of values for y = 4 x - 3:
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| y |
Complete the table of values for y = 4 - 3 x:
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| y |
Find the gradient of y = 4 x - 3.
Find the gradient of y = 4 - 3 x.
Graph the two equations on the same set of axes.
Using your answer from part (e), find the point of intersection of the lines.
Consider the following system of equations:
Find the gradient, and the y-value of the y-intercept, of the line y = x - 2.
gradient
y-value of the y-intercept
Find the gradient, and the y-value of the y-intercept, of the line y = - 3 x - 6.
gradient
y-value of the y-intercept
Graph the two equations on the same set of axes.
State the coordinate pair \left(x, y\right) that satisfies both equations.
Consider the following system of equations:
\begin{aligned} y &= - 4 x - 1 \\ y &= - 4 x + 2 \end{aligned}
Graph the two equations on the same set of axes.
Does there exist a value for x and y that satisfy the following two equations simultaneously?
For each of the following systems of equations:
Graph the two equations on the same set of axes.
State the values of x and y that satisfy both equations.