Given the system of linear equations.
1 answer:
Part A: The solution of the system of equations is (3 , -2)
Part B: (3 , -2) is the solution of the system of equations because it is satisfied the two equations
Part C: (3 , -2) is the solution of the system of equations because the two line which represent the equations intersect each other on it
Step-by-step explanation:
The system of equation is:
- x - y = 5
- 4x + y = 10
Part A:
∵ x - y = 5
- Add y to both sides to ind x in terms of y
∴ x = 5 + y ⇒ (1)
∵ 4x + y = 10 ⇒ (2)
- Substitute x in equation (2) by equation (1)
∴ 4(5 + y) + y = 10
- Multiply the bracket by 4
∴ 20 + 4y + y = 10
- Add like terms
∴ 20 + 5y = 10
- Subtract 20 from both sides
∴ 5y = -10
- Divide both sides by 5
∴ y = -2
- Substitute the value of y in equation (1) to find x
∵ x = 5 + (-2)
∴ x = 5 - 2
∴ x = 3
The solution of the system of equations is (3 , -2)
Part B:
To verify the answer above substitute x and y in each equation to prove that the left hand side and the right hand side of each equation are equal
In equation x - y = 5
L.H.S ⇒ x - y = 3 - (-2) = 3 + 2 = 5
∵ L.H.S. = 5
∵ R.H.S. = 5
∴ L.H.S. = R.H.S.
∴ (3 , -2) is a solution of the equation
L.H.S ⇒ 4x + y = 4(3) + (-2) = 12 - 2 = 10
∵ L.H.S. = 10
∵ R.H.S. = 10
∴ L.H.S. = R.H.S.
∴ (3 , -2) is a solution of the equation
(3 , -2) is the solution of the system of equations because it is satisfied the two equations
Part C:
From the attached graph
The red line represents the equation x - y = 5
The blue line represents the equation 4x + y = 10
∵ The two lines intersect each other at point (3 , -2)
∴ (3 , -2) is the solution of the system of equations
(3 , -2) is the solution of the system of equations because the two line which represent the equations intersect each other on it
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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