# Solve the system of linear equations -x+y=1 2x+y=-2Solve the system of linear equations -x+y=1 2x+y=-2

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-x + y = 1 .......(1)

2x +y = -2.......(2)

using the elimination method, subtract (1) from (2):

==> 3x = -3

==> x = -1

Now using the substitution method, substitute with x value in either equations.

-x + y = 1

==> y= x+1

==> y= -1+1 = 0

==> y =0

-x+y = 1.............(1)

2x+y =-2...........(2)

Solution:

We can eliminate y subtraction and solve for x . Also we can eliminate x by adding 2*eq (1) and eq(2) and solving for y.

We go her by substitution method.

From eq (2) we get y = -2-2x. Substitute this value of y in eq(1).

-x+(-2-2x) = 1

-x+2x -2 = -1

x = -1+2 = 1. Put x=1 in eq(1):

-1+y =1

y = 1+1 =2

x =1 and y =2.

The given equations are:

-x+y=1 .....................(1)

2x+y=-2.....................(2)

Subtracting (1) from (2), 2x-(-x)+y-y=-2-1 or 3x=-3 , x=-1

Substitute this in (1), 1+y=1 or y=0.

The solution of the given linear equations is x=-1 and y=0.

We'll solve the system using the elimination method.

We'll note the equations of the system as:

-x + y = 1 (1)

2x + y = -2 (2)

We'll multiply (1) by 2:

2*(-x + y) = 2*1

We'll remove the brackets:

-2x - 2y = 2 (3)

We'll add (3) to (2):

2x + y - 2x - 2y = -2 + 2

We'll eliminate like terms:

-y = 0

**y = 0**

We'll substitute y=0 in the equation (2):

2x + y = -2 => 2x + 0 = -2 => 2x = -2

We'll divide by 2:

**x = -1**

**The solution of the system is: {(-1 , 0)}.**