IGCSE /Grade 10
Maths MCQ Based On Finding the number of solutions to simultaneous equations
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IGCSE Grade 10 Maths Finding the number of solutions to simultaneous equations
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Solve the system using the elimination method.
A system of linear equations has one solution when the graphs intersect at a point.
A system of linear equations has no solution when the graphs are parallel.
Let's find the slopes of both equations by rearranging them in slope-intercept form (y = mx + b).
Check the gradients and y intercept.
Compare the gradients and y - intercept to find the solution.
The relationship between the number of variables and equations provides information about the potential number of solutions, but it does not guarantee a specific outcome.
We can notice that Equation 2 is exactly twice Equation 1. This means that Equation 2 is a multiple of Equation 1. Therefore, the two equations represent the same line, and they are coincident.
Find the gradient and y-intercept.
Find the gradient and the y-intercepts for the given simultaneous equations.
Given system of equations: x + 2y = 3 (Equation 1) 2x + 4y = 6 (Equation 2)
We can simplify Equation 2 by dividing both sides by 2: x + 2y = 3 (Equation 1) x + 2y = 3 (Equation 2 simplified).Upon simplification, we can see that both equations represent the same line. When graphed, they will overlap completely since they are identical.
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