SOLUTION: i have to solve the problems using system of equations.. 1.x+y=6 2. 2x-3y=-13 y=2x y=2x+7

Question 69431: i have to solve the problems using system of equations..
1.x+y=6 2. 2x-3y=-13
y=2x y=2x+7
Answer by mathick(4) (Show Source): You can put this solution on YOUR website!
Let's start with #1:
x + y = 6
y = 2x.

There are a few ways to solve these, but the substitution method is often easiest.

1. Substitute 2x in for y in the 1st equation: x + (2x) = 6.
(This can be done because the 2nd equation says y and 2x are interchangeable).

2. Simplify: 3x = 6.

3. Solve for x: x = 2.

4. Plug 2 in for x in the 1st equation: 2 + y = 6.

5. Solve for y: y = 4.

6. Final Answer: (2, 4). (x = 2, y = 4).

That's the substitution method - the next example has a few more steps:

2x-3y=-13
y=2x+7

1. Substitute 2x + 7 in for y in the 1st equation: 2x - 3(2x + 7) = -13.
(This can be done because the 2nd equation says y and 2x + 7 are interchangeable).

2. Simplify: -4x - 21 = -13.

3. Solve for x: x = -2.

4. Plug -2 in for x in the 1st equation: 2(-2) - 3y = -13.

5. Solve for y: y = 3.

6. Final Answer: (-2, 3). (x = -2, y = 3).
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