Question

What is the solution of 3x + 5 = 2x – 7?

A. the x-coordinate of the intersection point of the lines y = 3x + 5 and y = 2x – 7
B. the x-coordinates of the x-intercepts of the lines y = 3x + 5 and y = 2x – 7
C. the y-coordinate of the intersection point of the lines y = 3x + 5 and y = 2x – 7
D. the y-coordinates of the y-intercepts of the lines y = 3x + 5 and y = 2x – 7

Answer 1

Its option A
where the lines intersect x satisfies both y = 3x+5 and y = 2x - 7

Answer 2

Keywords:

System of equations, ordered pair, variable, graphic solution

For this case we have the following equation:
`3x + 5 = 2x - 7`, which we can rewrite as a system of two equations with two variables of the form:

`y = 3x + 5\\y = 2x-7`

• Algebraic solution:

We equate the equations, obtaining
`3x + 5 = 2x - 7`. From here we can clear the value of "x", then substitute in any of the two equations and find the value of "y". Thus, we obtain the ordered pair
`(x, y)`which is the solution of the system of equations.

• Graphic solution:

We graph both equations. The solution of the system of equations is the point of intersection
`(x, y)` of both lines.

So, we have that the solution of
`3x + 5 = 2x - 7` is the x - coordinate of the intersection point of the lines
`y = 3x + 5` and
`y = 2x - 7`

Answer:

The x-coordinate of the intersection point of the lines
`y = 3x + 5` and
`y = 2x - 7`