Solve the simultaneous equations: 3x + 4y = 5 , 2x - 3y = 9
To solve the equations the first step to take is to eliminate one of the variables x or y so we can get the value of it and then substitute it back in to get the value of the other.
One way to do this would be to multiply the first equation by 2 in order to get 6x + 8y = 10, and the second by 3 to get 6x - 9y = 27. This allows us to subtract one equation from the other and eliminate the x value to leave us with y. So let's subtract the second equation from the first, this results in the equation 17y = -17. We can simplify this down by dividing by 17 on both sides to get y = -1.
Finally substitute y = -1 back into either equation to find x. Take the first for example: 6x + 8(-1) = 10 (substitute y = -1 in)6x - 8 = 10 (+8 both sides)6x = 18 (divide by 3 both sides)x = 3
Answer: x = 3, y = -1
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