1. solve the system of equations algebraically. -2x + 5y = -2 x - 3y = 3 2. solve the system of equations algebraically. 5x + 3y = 30 3x + 3y = 18 3. find the solution to the system of equations algebraically: 2x - 2y + z = -15 6x - 3y- z = -19 3x - y - z = -6

1. We can double the second equation to get: 2x - 6y = 6; and then add the equations together to get -y = 4, y = -4. We plug y in to get x - 3(-4) = 3, x = 15. The answer would be (15, -4)
2. We can subtract the two equations to eliminate y and get 2x = 12, x = 6. We can plug x in to the second equation to get 9 + 3y = 18, and 3y = 9, so y = 3. The answer would be (6, 3)
3. We add the first two equations to get 8x - 5y = -34, and then subtract the last two equations to get 3x - 2y = -13. We multiply the first by 2, and the second by 5, and then add them together. We get x = -3. We plug the x-value into the second equation to get -9 - 2y = -13, so y = 2. We plug both values into the third equation to get -9 - 2 - z = -6. -z = 5, z = -5.
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Hope this helps!
==jding713==