Solutions to a Line

Identify the number of solutions for the equation below:

• No Solution

• One Solution

• Infinite Solutions

Which of the following is a solution to the graphed equation above?

• (3, 2)

• (-4, 6)

• (1, 3)

• (3, 1)

Which of the following is a solution to the equation
2x + 3y = 12

• (0, 3)

• (3, 2)

• (2, 0)

• (-1, -4)

Which of these is a solution to the equation
y = 5x?

• (1,5)

• (1, -5)

Determine the values of x and y that satisfy the equations: 7x - 2y = 5 and 3x + 4y = 11

• x = 4, y = 3

• x = 2, y = 4

• x = 3, y = 2

• x = 5, y = 1

9. Determine the values of x and y that satisfy the equations: 6x + 2y = 14 and 3x - 5y = 1

• x = 3, y = 4

• x = 2, y = 5

• x = 1, y = 7

• x = 5, y = 2

Identify the option having two correct solutions for the equation 5x + 4y = 20

• (2,1) and (3,2)

• (1, 4) and (3,1)

• (0, 5) and (4, 0)

• (4, 3) and (3, 0)

Answer explanation

5x + 4y = 20 On taking (x = 0, y = 5), L.H.S = 5(0) + 4(5) = 20 = R.H.S On taking (x = 4, y = 0), L.H.S = 5(4) + 4(0) = 20 = R.H.S Therefore, (0, 5) and (4, 0) are two solutions of the given linear equation in two variables.

Find the solution to the system of equations: 4x - 3y = 5 and 2x + 7y = 1

• x = 2, y = -1

• x = -1, y = 2

• x = 5, y = 3

• x = 3, y = 4

Determine the values of x and y that satisfy the equations: 7x - 2y = 5 and 3x + 4y = 11

• x = 4, y = 3

• x = 2, y = 4

• x = 3, y = 2

• x = 5, y = 1

Determine the values of x and y that satisfy the equations: 6x + 2y = 14 and 3x - 5y = 1

• x = 3, y = 4

• x = 2, y = 5

• x = 1, y = 7

• x = 5, y = 2