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2x-y=3 x+2y=-6

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3 Answers

2x-y=3
x+2y=-6
multiply the second equation by -2
-2x-4y=12
add the first equation and the new second equation
2x-y=3
-2x-4y=12
-5y=15
y=-3
substitute into the first equation
2x-(-3)=3
2x+3=3
2x=0
x=0
solution:(0,-3)
 
using substitution...
2x-y=3
x+2y=-6
x=-2y-6
substitute into the first equation
2(-2y-6)-y=3
-4y-12-y=3
-5y-12=3
-5y=15
y=-3 again,
substitute into the first equation
2x-(-3)=3
2x+3=3
2x=0
x=0 again
these are just two ways to solve the problem; you can solve it in other ways:you can multiply the first equation by 2 and take it from there or solve for y in the first equation and then substitute into the second equation
Hi Roseland,
 
2x-y=3    equation 1
 
x+2y=-6  equation 2
 
solving equation 1, we get
2x-3=y   
 
substitute the value 0f y=2x-3 in equation 2
 
x+2y=-6
x+2(2x-3)=-6
 
x+4x-6=-6
 
5x=-6+6
 
5x=0
x=0
 
y=2x-3=2(0)-3=0-3=-3
 
 
The solution to the given system of equations is x=0 and y=-3
2x - y = 3
x + 2y = -6

R1 2, -1, 3
R2 1, 2, -6

R1 > R1 - 2*R2

R1 0, -5, 15
R2 1, 2, -6

R1 > R1 / (-5)

R1 0, 1, -3
R2 1, 2, -6

R2 > R2 - 2*R1

R1 0, 1, -3
R2 1, 0, 0

0x + y = -3
x + 0y = 0

y = -3
x = 0

check:

2(0) - (-3) = 3 √
(0) + 2(-3) = -6 √

[Why keep writing the variables when all the information is in the coefficients and constants?]

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