Hi, everyone! Welcome to another Harrow School 13 plus video. Today, we’re diving into some simultaneous equations. It’s a bit of a tricky one, and it can look quite intimidating at first. We’ve touched on simultaneous equations before, perhaps during a perimeter question, but today’s problem appears more challenging for many students.
So, why does this particular question seem so daunting? Well, it’s because it includes fractions combined with simultaneous equations, which can be a nerve-wracking combo. Let’s break it down and see how we can solve it step by step.
Breaking Down the Equations
Here’s the first equation we need to tackle:
y = 7/x
And the second equation is:
y – 3 = 9/x
Methods to Solve Simultaneous Equations
There are several ways to solve simultaneous equations:
- Elimination Method
- Substitution Method
- Graphical Method (though we won’t cover this today)
In the past, we’ve used the elimination method, but for today’s problem, we’ll go with the substitution method. It’s given us a head start by specifying y = 7/x, making substitution a practical choice.
Substituting the Values
We substitute ( y ) in the second equation with y = 7/x:
y – 3 = 9/x
Simplifying the Equation
Let’s multiply both sides by ( x ) to get rid of the fractions:
[ 7 – 3x = 9 ]
This simplification process is crucial because it reduces the equation by eliminating fractions, leaving us with a more manageable expression.
Solving for ( x )
Let’s solve for ( x ):
- Add ( 3x ) to both sides:[ 7 = 9 + 3x ]
- Subtract 9 from both sides:[ 7 – 9 = 3x ]
- Divide both sides by 3: x =(-2/3)
Finding ( y ) from ( x )
Now, we can substitute ( x =-2/3 ) back into the first equation to find ( y ):
[ y = 7 / (-2/3) ]
Simplifying ( y )
Simplify the above fraction:
[ y = 7 x – 3/2 = y = -21/2 ][ y = -10.5 ]
Summarising the Solutions
So, we have our two solutions:
- ( x = – 2/3 )
- ( y = -10.5 )
And that’s it! We successfully tackled a seemingly daunting problem step by step. Remember, practice is key. These methods become easier with time and exposure.
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