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# What is the x-coordinate of the solution to the system x+y=5X-2y=-1

Hello, here's the solution to your problem:

x + y = -1

5x - 2y = -1

1) Solve for x for the first equation: y = -x -1

2) Substitute that value for y into the second equation: 5x - 2(-x-1) = -1

3) Solve for x: 7x = -3 => x =  -3/7

x+y = 5X-2y = -1 (This is really saying that these three things all are equal.)

• x + y = -1
• 5x - 2y = -1
• x + y = 5x -2y

There are a couple of different ways we can solve this.

Substitution:

1. x + y = -1
2. y = -x - 1 (subtract x from both sides)
3. 5x - 2y = -1
4. 5x -2*(-x - 1) = -1 (substitute for y from line 2.)
5. 5x +2x +2 = -1 (Distribute multiplication over addition with the -2) [Check the signs on this]
6. 7x + 2 =  -1 (combine like terms)
7. 7x = -3 (subtract 2 from both sides)
8. x = -3/7 (divides both sides by 7)

This time we will use more than one equation at a time.

• x + y = -1
• 5x - 2y = -1
• We're trying to find a way to get rid of the y variable.
1. 2x + 2y = -2 (multiply both sides of the first equation by 2)
2. 5x - 2y = -1 (I'm going to add these two equations together)
3. 2x +5x + 2y - 2y = -2 + -1 ( add the left sides and the right sides)
4. 7x = -3 (combine like terms)
5. x = -3/7 (divide both sides by 7)

Here is a quick way to solve it.  Remember (-1) is equal to (-1).  That's the reflexive property.  Though I always liked to call it the "no duh" property.

But moving right along:  X + Y = 5x - 2y        ...we know this, now...

If we add 2y to each side:    X + 3y = 5x     .....good, now let's subtract X from each side...

Then we will get:        3y = 4x     ....and if we solve for Y we get:

Y = (4/3)x   ...Now we are ready to plug these in and solve.

X + Y = -1   now becomes:  X + (4/3)X = -1

Let's combine like therms One plus four thirds is one and four thirds so..

(7/3)x = -1

We arrive at our answer by multiplying by the RECIPROCAL of the X coefficient:

X = -(3/7)