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