Question

what is the slope,y intercept ,are the lines the same intersecting ,or parallel? What are the number of solutions? Classification ,Consistent-dependent,Consistent-independent,or Inconsistent? use y = mx + b ,m = slope ,b = y-int for y = 2x + 3, 2x - y = 5 and 3x - y = 5 ,2x + y = -3 and y = x + 4 ,y = x + 4. Ive tried posting this question a few times but cannot get the right wording plz help me

Answer 1

Answer:

1. For equation:  y = 2x + 3 , 2x - y = 5 There is no solution to this system of equations.
2. For equation: y = 2x + 3 ,  2x - y = 5 There is one solution to the system of equations.
3. For equation: y  = x + 4 , y  = x + 4 There are infinite solutions to the system.

Step-by-step explanation:

• The equation of straight line is written as y = m x + c where 'm' is slope.
• y - intercept of line is value which intersect the point on y-axis.
• To find y -intercept , put x = 0 in equation.
• If slope of two lines are equal then lines are parallel.
• If the lines are not parallel, they will always intersect

For equation:  y = 2x + 3 , 2x - y = 5

Compare equation y = 2x + 3 with y = m x + c then we get slope 'm' is 2.

Now, put x = 0 in y = 2x + 3 to get y-intercept

y = 2(0)+ 3

y = 0 + 3

y =  3

so, the y-intercept is 3 .

Re-write this equation 2x - y = 5 in the slope intercept form;

Subtract 2x from both the sides of 2x - y = 5

2x - y - 2x = 5 - 2x

- y = - 2x + 5

Multiply both the sides by '-1'

y = 2x - 5

so, when we compare above equation with y = m x + c then we get slope 'm' is 2 .

Now, put x = 0 in y = 2x - 5 to get y-intercept

y = 2(0) - 5

y = 0 - 5

y =  - 5

so, the y-intercept is - 5 .

Equation y = 2x + 3 and  2x - y = 5 are parallel (since there slope are equal 'm = 2').

There is no solution to this system of equations.

For equation:  3x - y = 5 , 2x + y = -3

Re-write this equation 3x - y = 5 in the slope intercept form;

Subtract 3x from both the sides of 3x - y = 5

3x - y - 3x = 5 - 3x

- y = - 3x + 5

Multiply both the sides by '-1'

y = 3x - 5

so, when we compare above equation with y = m x + c then we get slope 'm' is 3 .

Now, put x = 0 in y = 3x - 5 to get y-intercept

y = 3(0) - 5

y = 0 - 5

y =  - 5

so, the y-intercept is - 5 .

Re-write this equation 2x + y = -3 in the slope intercept form;

Subtract 2x from both the sides of 2x + y = -3

2x - y - 2x = -3 - 2x

- y = - 2x - 3

Multiply both the sides by '-1'

y = 2x + 3

so, when we compare above equation with y = m x + c then we get slope 'm' is 2 .

Now, put x = 0 in y = 2x + 3 to get y-intercept

y = 2(0) + 3

y = 0 + 3

y =  3

so, the y-intercept is 3 .

Equation 3x - y = 5 and 2x + y = -3 are intersecting lines (since their slope are not equal).

There is one solution to the system of equations (since the lines are intersect).

For equation:   y  = x + 4 , y  = x + 4

Compare equation y = x + 4 with y = m x + c then we get slope 'm' is 1.

Now, put x = 0 in y = x + 4 to get y-intercept

y = 0+ 4

y =  4

so, the y-intercept is 4 .

since equation of line are same therefore slopes are also equal

Equation  y  = x + 4 and y  = x + 4 are parallel lines.

There are infinite solutions to the system. ( Since equivalent equation)