2x+5y=9, 2x+4y=3 solve by crimers rule
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 = 19 simultaneous equations 3x + 4y = 19
2) 2x − y = 9 simultaneous equations 8x − 4y = 36
simultaneous equations
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 with (5, 1) in the original equations.