A system of linear equations includes the line that is created by the equation y = x+ 3, graphed below, and the line through the points (3, 1) and (4, 3). On a coordinate plane, a line goes through (0, 3) and (2, 5).
What is the solution to the system of equations?

  (8, 11)

Step-by-step explanation:

The 2-point form of the equation of a line is useful for the one where only points are given.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (3 -1)/(4 -3)(x -3) +1

  y = 2(x -3) +1

We can equate this to the expression for y in the given equation.

  x +3 = 2(x -3) +1

  x +3 = 2x -5 . . . . . . eliminate parentheses

  8 = x . . . . . . . . . . . . add 5-x

Using the given equation, we can find y:

  y = x +3 = 8 +3

  y = 11

The solution to the system is (x, y) = (8, 11).

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.