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Solving simultaneous equations graphically. Slideshow 32, Mathematics Mr Richard Sasaki, Room 307. Objectives. Consider the two methods learned previously regarding how to draw graphs Understand how to find unique solutions for simultaneous equations represented graphically. Drawing Lines.
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Solving simultaneous equations graphically Slideshow 32, Mathematics Mr Richard Sasaki, Room 307
Objectives • Consider the two methods learned previously regarding how to draw graphs • Understand how to find unique solutions for simultaneous equations represented graphically
Drawing Lines If we are given an equation in any format (let’s say as we’re dealing with simultaneous equations, do draw a line we can either… • Change the subject • Find two pairs of co-ordinates Both are necessary so we will practice using both. Let’s start with changing the subject.
Simultaneous equations – changing the subject Let’s try an example. Graphically, solve the simultaneous equations and . Firstly, let’s rearrange both. Next, let’s draw these lines!
Simultaneous equations – changing the subject First, let’s draw and label . And next . What do we do next? Right! Find the co-ordinates where the lines cross… We get (5, 3), so…
How many solutions? When two lines are on top of each other… When two lines cross… When two lines are parallel… Hopefully you found out… We get one solution. We get no solutions. We get infinite solutions!
Solving simultaneous equations graphically One problem with solving simultaneous equations graphically… Or this?? How do we solve this?? Our pencils and eyes aren’t accurate enough sometimes. So we’d need to calculate them another way.
Solving simultaneous – Finding Two Pairs of co-ordinates If you recall from last time, the ideal two pairs of co-ordinates to find are the following… This way, we can remove one unknown from each equation and calculate the other. We need to do this for both lines.
Solving simultaneous – Finding Two Pairs of co-ordinates Let’s use the same example as before. Graphically, solve the simultaneous equations and . So we need two pairs of co-ordinates for each line. … … … …
Solving simultaneous – Finding Two Pairs of co-ordinates So for we get (0, 8) and (8, 0). For we get (0, -2) and (2, 0). Let’s connect points (0, 8) and (8, 0) first and label. Next, let’s connect points (0, -2) and (2, 0) and label. Once again, we can see that the lines cross at (5, 3). So .
