Two simultaneous questions are given as 3x+2y = 9, and x-2y = -5. Find the values for x and y

Can be solved in 3 ways:
Substitution - can rearrange equation 2 to for x = 2y-5. Then substitute this in to equation 1 to form, 3(2y-5)+2y = 9. Multiply out the brackets and rearrange to form 8y = 24, so y=3 (would be explained step by step on whiteboard). Then substitute value for y into the equation: x-2(3)= -5, so x-6= -5, therefore x = 1.
Elimination:Alternate signs for y in each equation, so can add the equations together to cancel them out. This would form 4x = 4, therefore x = 1. Then substitute in the x value into one of the equations (same principle as in substitution method), 1-2y = -5. 2y = 6, therefore y = 3.
Graph:Could draw a graph for each line, and see the x and y co-ordinates at which they intersect. Good method for visualising the concept of solving the equation, but not time-efficient.

AS
Answered by Aman S. Maths tutor

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