solve the following simultaneous equation using Cramer's rule
3x-4y=10;4x+3y=5
Answers
Answer:
If we add the equations as they are, neither one of the unknowns will cancel. Now, if the coefficient of y in equation 2) were −4, then the y's would cancel. Therefore we will expand our strategy as follows:
Make one pair of coefficients negatives of one another -- by multiplying
both sides of an equation by the same number. Upon adding the equations, that unknown will be eliminated.
To make the coefficients of the y's 4 and −4, we will multiply both sides of equation 2) by 4 :
1) 3x+4y=193x+4y=19 2) 2x−y=98x−4y=36 11x =55 x=55
11 x=5
The 4 over the arrow in equation 2) signifies that both sides of that equation have been multiplied by 4. Equation 1) has not been changed.
To solve for y, substitute x = 5 in either one of the original equations. In equation 1):
3· 5 + 4y=19 4y=19 − 15 4y=4 y=1
The solution is (5, 1).
The student should always verify the solution by replacing x and y
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