-2(-6x-6)=3(4x+5)-3

While solving an equation for the variable y, Garo is left with the equation 3=7. Assuming all this work was done correctly, what can garo conclude about the solution to his equation?

One solution: if at least the coefficients of one of the two variables are different ⇒ (two intersected lines)
No solution: if the coefficients of the two variables are equal and the numerical terms are different ⇒ (two parallel lines)
Many solutions if the simplest form of the two equations are equal ⇒ (two coincide lines)

-2(-6x - 6) = 3(4x + 5) - 3

That means the system of equations is

y = -2(-6x - 6)

y = 3(4x + 5)

∵ Garo solved it for the variable y and left with 3 = 7

- That means when he puts any value of x in the equation, the left hand

side gives 3 and the right hand side gives 7

- Assuming all this work was done correctly

∵ The two sides of the equation are not equal

∴ The two equations have same coefficients of x and y and different

numerical terms

∴ There is no solution for his equation

Garo can conclude that his equation has no solution

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