Question

Solve x + 3y = 9 3x – 3y = -13 (1 point)

Answer 1

Answer:

(-1, 10/3)

x = -1

y = 10/3

Step-by-step explanation:

To solve a system, one of the methods you can use is elimination. To use elimination, you need a variable to have the same coefficient in BOTH equations. Since both equations have "3y", with the same coefficient (3), we can use this method.

We want to eliminate a variable by cancelling it out. Since positive 3y PLUS negative 3y is 0, the variable in eliminated. ADD each of the terms in the equations together.

.        x + 3y = 9

+    3x – 3y = -13

.     4x – 0y = -4           3y - 3y = 0        

.             4x = -4            Divide both sides by 4 to isolate 'x'

.               x = -1              Solved for the x-coordinate

Since we know one variable, 'x', we can easily find the other, 'y'. Substitute 'x' with -1 in any of the equations. Then, isolate 'x'.

x + 3y = 9

(-1) + 3y = 9

-1 + 1 + 3y = 9 + 1      Add 1 to both sides to cancel out left side.

3y = 9 + 1          Add on the right side (9 + 1 = 10)

3y = 10              Divide both sides by 3 to isolate 'y'

y = 10/3             Solved for the y-coordinate

Put the 'x' and 'y' coordinates together in an ordered pair, which you write as (x, y).

The solution to the system is (-1, 10/3).