Question

v) Verity the consistency of following equation.
2X + 2Y = -2, X + Y = -1, 3X + 5 Y = -5​

Answer 1

Equation 1: 2X + 2Y= -2

Equation 2: X+Y =-1

Equation 3: 3X+5Y=-5

There are several ways you can approach this question. How about direct substitution? The way you can prove the consistency is by isolating any one variable and then substituting it into other equations to confirm whether or not LHS=RHS.

From Equation 2, take X= -1-Y. Now that we have isolated X, substitute it into Equation 1: 2X+2Y=-2

2(-1-Y) +2Y=-2

-2-2Y+2Y=-2

-2=-2

LHS=RHS. It is consistent

Similarly for Equation 3: 3X+5Y=-5

3(-1-Y)+5Y=-5

-3-3Y+5Y=-5

-3+2Y=-5

2Y= -2

Y=-1. We're getting Y=-1, let's put this in equation 2 to check if LHS=RHS

So, Equation 2: X+Y=-1

-1-Y+Y=-1

-1+1-1=-1

-1=-1

LHS=RHS

Indeed!

Yes, it is consistent. Hence verified.

Answer 2

Step-by-step explanation:

2x+2y=-2,x+y=-1,3x+5y=-5