Question

What is the solution to the system of equations?

2x + y = -3
x - 2y = -4

( __ , __ )

Answer 1

Answer: x=-2 y=13

2(-2)+1=-3 check

-2-2=-4 check

Explanation:

Horner's method:

2 1 -3

1 -2 -4

delta = det(

2 1

1 -2) = 2×-2 - 1 = -5

x = det(

-3 1

-4 -2)/-5 = (-2×-3-1×-4)/-5 = -2

y = det(

2 -3

1 -4)/-5 = (-8+3)/-5 = 1

Or by elimination

x = 2y - 4 from adding 2y=2y to second eqn

2(2y-4)+y=-3 by substituting for x in first.

4y-8+y=-3

5y=8-3=5

y=1

x=2y-4=2-4=-2

Answer 2

(-2,1)

Explanation:

2x + y = -3

x - 2y = -4

Multiply the first equation by 2 so we can eliminate y

2(2x + y = -3 )

4x +2y = -6

Add the second equation

4x +2y = -6

x - 2y = -4

-------------------

5x = -10

Divide by 5

5x/5 = -10/5

x = -2

We still need to find y

2x + y = -3

Substitute x in

2(-2) +y = -3

-4 +y = -3

Add 4 to each side

-4+4 +y = -3+4

y = 1