Mimi198
contestada

Consider the system of linear equations.
2y = x + 10
3y = 3x + 15
Which statements about the system are true? Check all that apply.
The system has one solution.
The system graphs parallel lines.
Both lines have the same slope.
Both lines have the same y-intercept.
The equations graph the same line.
The solution is the intersection of the 2 lines

Respuesta :

the first one, the fourth one, and the last one

The following statement are correct about the system of equation:

  • Both lines have the same y-intercept.
  • The solution is the intersection of the 2 lines
  • The system has one solution

2y = x + 10

3y = 3x + 15

Point slope form:

  • y = mx + b

where

m = slope

b = y-intercept

Let put it in point slope form.

2y = x + 10

y =  1 / 2 x + 5

slope = 1 /2

y-intercept = 5

3y = 3x + 15

y = x + 5

slope = 1

y-intercept = 5

Let's solve the combined equation;

2y - x = 10

3y - 3x = 15

6y - 3x = 30

3y = 15

y = 15 / 3

y = 5

3(3) - 3x = 15

9 - 3x = 15

-3x = 15 - 9

-3x = - 6

x = -6 / -3

x = 2

Therefore,

  • Both lines have the same y-intercept.
  • The solution is the intersection of the 2 lines
  • The system has one solution

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