The ordered pair (0 , 3) satisfies the system of equations
x = y - 3 and x/2 + 2y = 6
Step-by-step explanation:
To find the ordered pair(x , y) satisfies a system of equations
1. Use the elimination method or the substitution method to find the
the value of x or y
2. Substitute the value of x or y in one of the 2 equations to find y or x
3. Substitute the values of x and y in each equation to check if they
satisfy the system of equations or not
∵ x = y - 3 ⇒ (1)
∵ [tex]\frac{x}{2}[/tex] + 2y = 6 ⇒ multiply all terms of the equation by 2
∴ x + 4y = 12 ⇒ (2)
Substitute x in equation (2) by equation (1)
∵ (y - 3) + 4y = 12
∴ y - 3 + 4y = 12
- Add the like terms in the left hand side
∴ (y + 4y) - 3 = 12
∴ 5y - 3 = 12
- Add 3 to both sides
∴ 5y = 15
- Divide both sides by 5
∴ y = 3
Substitute the value of y in equation (1)
∵ x = y - 3
∵ y = 3
∴ x = 3 - 3
∴ x = 0
∴ The ordered pair (0 , 3) is the solution of the system of the equation
Let us check the answer by substituting x and y in each equation
∵ x = y - 3
∵ x = 0 and y = 3
∴ 0 = 3 - 3
∴ 0 = 0
∴ Left hand side = right hand side
∵ [tex]\frac{x}{2}[/tex] + 2y = 6
∵ x = 0 and y = 3
∴ [tex]\frac{0}{2}[/tex] + 2(3) = 6
∴ 0 + 6 = 6
∴ 6 = 6
∴ Left hand side = right hand side
∴ The ordered pair (0 , 3) satisfies the system of equations
x = y - 3 and x/2 + 2y = 6
The ordered pair (0 , 3) satisfies the system of equations
x = y - 3 and x/2 + 2y = 6
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