Question

You can solve the equation 4x – 7 = 5 by graphing y = 4x – 7 and y = 5 and finding their point of intersection. Use the drop-down menus to complete the statements below.

Step one: (3,5) is a solution of A. Only 4x – 7 = 5 B. Only y=5 C. Both D. Neither


Step two: the solution to 4x – 7 = 5 is- A. 3,5 B. 5,3 C. 5 D. 3

Put some points in too.

Answer 1

Step one: (3, 5) is a solution of both y = 4x – 7 and y = 5.

Step two: The solution of 4x – 7 = 5 is 3.

Explanation:

Answer 2

Part 1) Option C. Both

Part 2) Option D. 3

Explanation:

we have

`y=4x-7` ----> equation A

`y=5` ----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both lines

Using a graphing tool

The solution is the point (3,5)

see the attached figure

Part 1) we know that

If a ordered pair is a solution of the system, then the ordered pair must satisfy both equations (makes true both equations), that means that the ordered pair is a solution of both equations

In this problem the ordered pair (3,5) is a solution of the system, so the ordered pair (3,5) is a solution of equation A and equation B

Verify

Substitute the value of x and the value of y in each equation

For x=3, y=5

Equation A

`y=4x-7`

`5=4(3)-7`

`5=5` ---> is true

so

The ordered pair is a solution of equation A

Equation B

`y=5`

`5=5` ---> is true

so

The ordered pair is a solution of equation B

therefore

The ordered pair is a solution of both equations

Part 2) Determine the solution of the expression

`4x-7=5`

The solution is the x-coordinate of the intersection point both lines

so

The solution is x=3