solve the equation by creamers rule 2x+3y=13,x+7y=23
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.
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Answer:
y=23/7,2x+3y=69/7,x=0
y=30/7,2x+3y=-8/7,x=-7