DETERMINE IF THE POINT IS A SOLUTION TO THE EQUATION

Determine whether the given point satisfies the given equation, or in other words the point lies on the graph of the line:

Problem 1 :

(2, 5), y = 4x - 3

Solution :

The given point is

(x, y) = (2, 5)

Substitute 2 for x and 5 for y in the given equation.

5 = 4(2) - 3

5 = 8 - 3

5 = 5

The point (2, 5) satisfies the equation. So, it is a solution and (2, 5) is on the line.

Problem 2 :

(3, -1), y = 2x - 7

Solution :

The given point is

(x, y) = (3, -1)

Substitute 3 for x and -1 for y in the given equation.

-1 = 2(3) - 7

-1 = 6 - 7

-1 = -1

The point (3, -1) satisfies the equation. So, it is a solution and (3, -1) is on the line.

Problem 3 :

(-4, 2), y = -x + 3

Solution :

The given point is

(x, y) = (-4, 2)

Substitute -4 for x and 2 for y in the given equation.

2 = 4 + 3

2 ≠ 7

The point (-4, 2) does not satisfy the equation. So, it is not a solution and (-4, 2) is not on the line.

Problem 4 :

(-1, 7), y = -2x + 5

Solution :

The given point is

(x, y) = (-1, 7)

Substitute -1 for x and 7 for y in the given equation.

7 = -2(-1) + 5

7 = 2 + 5

7 = 7

The point (-1, 7) does not satisfy the equation. So, it is not a solution.

Problem 5 :

(4, -1), y = -2x + 7

Solution :

The given point is

(x, y) = (4, -1)

Substitute 4 for x and -1 for y in the given equation.

-1 = -2(4) + 7

-1 = -8 + 7

-1 = -1

The point (4, -1) satisfies the equation. So, it is a solution.

Problem 6 :

(1, 6), y = -3x + 5

Solution :

The given point is

(x, y) = (1, 6)

Substitute 1 for x and 6 for y in the given equation.

6 = -3(1) + 5

6 = -3 + 5

6 ≠ 2

The point (1, 6) does not satisfy the equation. So, it is not a solution and (1, 6) is not lie on the line.

Problem 7 :

You have $110 in your lunch account and plan to spend $2.75 each school day.

a. Write a linear equation that represents the balance in your lunch account.

b. How many school days will it take to spend all of the money in your lunch account?

Solution :

a) Let x be the number of days and y be the balance in your account after x days.

y = 2.75x

b) Amount you have = $110

110 = 2.75x

x = 110/2.75

x = 40

So, number of school days is 40.

Problem 8 :

The equation

22 = 2y + x

represents the perimeter of a flower garden with length y (in feet) and width x (in feet). Solve for y. Then find the length of the flower garden when the width is 2 feet, 3 feet, and 4 feet.

Solution :

22 = 2y + x

Here x is the width and y is the length of the garden.

So, the length of the garden is 10 ft, 9.5 ft and 9 ft respectively.

Problem 9 :

The equation

0.60 = 0.05x + 0.10y

represents the number of nickels x and dimes y needed to add up to 60 cents. Solve for y. Then find the number of dimes that are needed to make 60 cents when the number of nickels is 0, 2, and 4.

Solution :

Given that, 

0.60 = 0.05x + 0.10y

Solving for y, we get

0.10y = 0.60 - 0.05x

y = (0.60/0.10) - (0.05x/0.10)

y = 6 - 0.5x