solve the system: x-2y = 5 2x-y = 3 solve the system: x-2y = 5 2x-y = 3
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calendarEducator since 2011
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You may also consider the alternative method, that uses determinants, such that:
x-2y = 5
2x-y = 3
Form the determinant of the system such that:
=
You need to find the variable x such that:
You need to find the variable y such that:
Hence, evaluating the solutions to the system yields and .
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calendarEducator since 2008
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starTop subjects are Math, Science, and Social Sciences
x-2y = 5 .........(1)
2x - y = 3 .........(2)
To solve the system , we will use the elimination method:
multiply (1) by -2 and add to (2);
==>-2x + 4y = -10
==> 2x - y = 3
==> 3y = -7
==> y= -7/3
==> x = 2y + 5
= 2(-7/3) + 5 = -14/3 + 15/3 = 1/3
==> x = 1/3
To determine the solutions of the system, we'll use the substitution method. We'll note the equatios of the system as:
x-2y = 5 (1)
2x-y = 3 (2)
We'll add 2y both sides in (1):
x = 2y + 5 (3)
We'll substitute (3) into (2):
2( 2y + 5) - y = 3
We'llremove the brackets;
4y + 10 - y = 3
We'll combine like terms:
3y = 3-10
3y = -7
We'll divide by 3:
y = -7/3
We'll substitute y in (3):
x = 2(-7/3) + 5
x = -14/3 + 5
x = (-14+15)/3
x = 1/3
The solution of the system is: {(1/3 ; -7/3)}.
x-2y =5.........(1) and 2x-y = 3............(2)
We can solve the equation by elimination:
(1) - 2*(2) eliminates y:
(x-2y) - 2(2x-y) = 5-2*3 = -1
x-2y -4x- (-2y) = -1
x-4x = -1
-3x = -1. Divide by 3.
x = -1/-3 = 1/3.
(2)-2*(1) eliminates x and we can solve for y:
2x-y - 2(x-2y) = 3-2*5 = 3-10 = -7
-y+4y = -7
3y = -7. Divide by 3
3y/3 = -7/3
y = -7/3.
Threfore x = 1/3 and y = -7/3.
Given:
x - 2y = 5 ... (1)
2x - y = 3 ... (2)
Multiplying equation (1) by 2:
2x - 4y = 10 ... (3)
Subtracting equation (3) from (2):
2x - 2x - y + 4y = 3 - 10
==> 3y = - 7
Dividing both sides by 3:
y = -7/3
Substituting this value of y in equation (1)
x - 2*(-7/3) = 5
==> x + 14/3 = 5
==> x = 5 - 14/3 = 1/3
Answer:
x = 1/3
y = -7/3
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