Use algebraic rules of equations to predict the solution type to the system of equations. include all of your work for full credit.
{x+y=-4
{y=2x-1

The solution of the two equations is (-1 , -3)

Step-by-step explanation:

* Lets revise how to solve the system of the linear equations

- We have two ways to do that

# Substitution method

# Elimination method

- Substitution method is to find one variable in terms of the other

  variable from one of the two equations, then substitute this value

  in the second equation

* Lets solve the problem by the substitution method

∵ x + y = -4 ⇒ (1)

∵ y = 2x - 1 ⇒ (2)

- In equation (2) we have y in terms of x

∴ Substitute (2) in (1)

∴ x + (2x - 1) = -4 ⇒ simplify ir

∴ x + 2x - 1 = -4 ⇒ add the like terms

∴ 3x - 1 = -4 ⇒ add 1 to both sides

∴ 3x = -3 ⇒ divide both sides by 3

∴ x = -1

- Substitute the value of x in equation (2)

∴ y = 2(-1) - 1 = -2 - 1 = -3

∴ The solution of the two equations is (-1 , -3)

* Lets check the answer

- Substitute the value of x-coordinate and y-coordinate in equation (1)

∵ The left hand side = (-1) + (-3) = -4

∵ The right hand side = -4

∴ The two sides equal each other

∴ (-1 , -3) is a solution of the equation x + y = -4

* Lets do the same in the second equation

∵ The left hand side = -3

∵ The right hand side = 2(-1) - 1 = -2 -1 = -3

∴ The two sides equal each other

∴ (-1 , -3) is a solution of the equation y =2x - 1

∴ (-1 , -3) is the solution of the two equations

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