In 1.02 we learned how to solve a simple system of equations using the graphical method, where we graphed each equation and found their point of intersection. Now we will consider systems of more complex linear equations. For example, how could we solve the following simultaneous equations?
$\frac{5x}{2}+y=\frac{7}{13}$5x2+y=713
$2x-3y=14$2x−3y=14
Finding the gradients and the $x$x- and $y$y-intercepts of these lines requires extra work. We can't just read these values directly from the equation as we would with equations in gradient-intercept form such as $y=3x-2$y=3x−2.
For cases like this, using technology is an effective way to solve the system of equations.
There are many ways of using technology to obtain graphs from equations. Some of them are listed here:
- There are a number of websites that can create graphs given equations, such as www.geogebra.org and www.wolframalpha.com.
- Some calculators (often referred to as graphing calculators) have the ability to plot graphs.
- There are many apps available for smartphones that can plot graphs from equations.
Practice questions
Question 1
Consider the equations $y=2x$y=2x and $y=-35-3x$y=−35−3x.
Plot the graphs of both equations using technology, and state the point of intersection in coordinate form.
Question 2
Consider the following equations:
$4x-3y=-22$4x−3y=−22
$-3x-2y=8$−3x−2y=8
Plot the graphs of both equations using technology, and state the values of $x$x and $y$y which satisfy both equations.
$x=\editable{}$x=
$y=\editable{}$y=
Question 3
Consider the system of equations below.
| Equation 1 | $3x-1.8y=4.7$3x−1.8y=4.7 |
| Equation 2 | $0.55x+0.6y=-0.04$0.55x+0.6y=−0.04 |
Solve the system using technology, and state the values of $x$x and $y$y that satisfy both equations. Give your answers correct to two decimal places.
$x=\editable{}$x=
$y=\editable{}$y=