Question

Given the system of linear equations.

Answer 1

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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