Use substitution to solve the system of equations. 18 = x – 3y 2x + 19 = –5y a. (3, –5) b. (6, 10) c. (–11, 9) d. infinitely many solutions

A. (3, -5)

Step-by-step explanation:

Use the first equation to find an expression for x. (Add 3y.)

x = 18 + 3y

Now, use this where x is in the second equation.

2(18 +3y) +19 = -5y

55 +6y = -5y . . . . . . . eliminate parentheses

55 +11y = 0 . . . . . . . . .add 5y

5 +y = 0 . . . . . . . . . . .divide by the coefficient of y

y = -5 . . . . . . . . . . . . . add -5; corresponds to answer choice A

Using the expression for x, we can find its value:

x = 18 +3(-5) = 3

The solution is (x, y) = (3, -5). . . . . . matches choice A

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: