The true statements are:
The ordered pair (−4 , 0) is a solution to the first equation because it makes the first equation true ⇒ 1st answer
The ordered pair (−4 , 0) is a solution to the second equation because it makes the second equation true ⇒ 2nd answer
The ordered pair (−4, 0) is a solution to the system because it makes both equations true ⇒ 4th answer
Step-by-step explanation:
To prove that point (a , b) is a solution of an equation
- Substitute x and y in the equation by a and b
- If the left hand side is equal to the right hand side, then the point is a solution of the equation
- If the left hand side doesn't equal the right hand side, the point is not a solution of the equation
∵ The system of equations is:
2x + y = -8 ⇒ (1)
x - y = -4 ⇒ (2)
The ordered pair is (-4 , 0)
Substitute x by -4 and y by 0 in each equation
∵ x = -4 and y = 0
∵ The left hand side in equation (1) is 2x + y
∵ 2(-4) + 0 = -8 + 0 = -8
∴ The left hand side = -8
∵ The right hand side = -8
∴ The left hand side = the right hand side
∴ (-4 , 0) is a solution of equation (1)
The ordered pair (−4 , 0) is a solution to the first equation because it makes the first equation true
∵ The left hand side in equation (2) is x - y
∵ (-4) - 0 = -4 - 0 = -4
∴ The left hand side = -4
∵ The right hand side = -4
∴ The left hand side = the right hand side
∴ (-4 , 0) is a solution of equation (2)
The ordered pair (−4 , 0) is a solution to the second equation because it makes the second equation true
∵ The ordered pair (-4 , 0) makes the two equations true
∴ The ordered pair (-4 , 0) is the solution of the system of equations
The ordered pair (−4, 0) is a solution to the system because it makes both equations true
Learn more:
You can learn more about the system of linear equations in brainly.com/question/6075514
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