Question

Two lines, A and B, are represented by the following equations: Line A: y = x − 1 Line B: y = −3x + 11 Which of the following options shows the solution to the system of equations and explains why? (3, 2), because the point does not lie on any axis (3, 2), because one of the lines passes through this point (3, 2), because the point lies between the two axes (3, 2), because both lines pass through this point Question 4(Multiple Choice Worth 4 points) (08.01) Line H is represented by the following equation: 2x + 2y = 8 What is most likely the equation for line K so the set of equations has infinitely many solutions? x + 2y = 2 x + y = 4 2x + y = 6 x − y = 8 Question 5(Multiple Choice Worth 4 points) (08.01) Line M is represented by the following equation: x − y = 8 Which equation completes the system that is satisfied by the solution (18, 10)? 2x − y = 26 x + y = 18 2x − 2y = 36 x − y = −28

Answer 1

1) The last one is correct.

Answer 2

Part 1. (3, 2), because both lines pass through this point.

Part 2. x + y = 4

Part 3. 2x − y = 26

Explanation:

Part 1.

The given system of equations are

`y=x-1`

`y=-3x+11`

Substitute the value of from one equation to another.

`x-1=-3x+11`

`x+3x=1+11`

`4x=12`

Divide both sides by 4.

`x=3`

The value of x is 3. Put this value in the given equation to find the value of y.

`y=3-1=2`

The value of y is 2. Both the equations satisfy by the point (2,3) it means the both lines pass through this point.

Therefore (3, 2) is the solution, because both lines pass through this point.

Part 2.

The given equation is

`2x+2y=8`

The set of equations has infinitely many solutions if both lines coincide each other.

Taking out the common factors.

`2(x+y)=8`

Divide both sides by 2.

`x+y=4`

The line
`x+y=4` is equivalent to
`2x+2y=8`. It means both line coincide each other and have infinitely many solutions.

Therefore the required equation of line is x + y = 4.

Part 3.

The one equation of the system of equations is

`x-y=8`

The solution of the system of equation is (18,10). It means both the equation are satisfied by the point (18,10).

Put x=18 and y=10 in each option.

`LHS=2x-y=2(18)-10=26=RHS`

`LHS=x+y=18+10=28\\eq RHS`

`LHS=2x-2y=2(18)-2(10)=16\\eq RHS`

`LHS=x-y=18-10=8\\eq RHS`

Therefore the required equation is 2x-y=26.