Question

Solve the system using a table
3y=4x+7
-4x-4y=28
(-4,-3)
(-3,-4)
(4,3)
(3,4)

Answer 1

To solve the system using a table, we can substitute the x and y values given in each pair of coordinates into the two equations and check if both equations are satisfied.

For the first coordinate (-4, -3):
3y = 4x + 7
3(-3) = 4(-4) + 7
-9 = -16 + 7
-9 = -9

-4x - 4y = 28
-4(-4) - 4(-3) = 28
16 + 12 = 28
28 = 28

Both equations are satisfied by the values (-4,-3).

For the second coordinate (-3, -4):
3y = 4x + 7
3(-4) = 4(-3) + 7
-12 = -12 + 7
-12 = -5

-4x - 4y = 28
-4(-3) - 4(-4) = 28
12 + 16 = 28
28 = 28

Both equations are satisfied by the values (-3,-4).

For the third coordinate (4, 3):
3y = 4x + 7
3(3) = 4(4) + 7
9 = 16 + 7
9 = 23
Both equations are not satisfied by the values (4,3).

For the fourth coordinate (3, 4):
3y = 4x + 7
3(4) = 4(3) + 7
12 = 12 + 7
12 = 19
Both equations are not satisfied by the values (3,4).

Therefore, the only solution to the system is (-4, -3).