classify the system of equations and identify the number of solutions

Question

2x+y=7

y+5= -2x

consistent dependent

infinte consistent

independent one

inconsistent none

inconsistent dependent one

Answer 1

The system of equations are 2x + y = 7 and y + 5 = - 2x.

To identify the number of solutions of the system by looking at the slopes and y-intercepts of the lines.

Write the each line equation in slope-intercept form y = mx + b, where m = slope and b = y-intercept.

 

Write Equation 1 : 2x + y = 7 in slope-intercept form.

Subtract 2x from each side.

2x + y - 2x = 7 - 2x

y = - 2x + 7.

 

Write Equation 2 : y + 5 = - 2x in slope-intercept form.

Subtract 5 from each side.

y + 5 - 5 = - 2x - 5

y = - 2x - 5.

 

Because the lines have the same slope but different y-intercepts, the system has no solution.This system is inconsistent.

The fourth option is correct.