In each of the following find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation:
`3-2x=7,2y+1=10-2 1/2y`

Answer

To find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation, we will solve each equation step by step.

### Step 1: Solve the first equation for x
The first equation is:
\[ 3 - 2x = 7 \]

To isolate \( x \), we first subtract 3 from both sides:
\[ -2x = 7 - 3 \]
\[ -2x = 4 \]

Next, we divide both sides by -2:
\[ x = \frac{4}{-2} \]
\[ x = -2 \]

Thus, the abscissa (x-coordinate) is -2.

### Step 2: Solve the second equation for y
The second equation is:
\[ 2y + 1 = 10 - 2\frac{1}{2}y \]

First, we need to convert the mixed fraction \( 2\frac{1}{2}y \) into an improper fraction:
\[ 2\frac{1}{2}y = \frac{5}{2}y \]

Now, rewrite the equation:
\[ 2y + 1 = 10 - \frac{5}{2}y \]

Next, we can eliminate the fraction by multiplying the entire equation by 2 (the denominator):
\[ 2(2y + 1) = 2(10 - \frac{5}{2}y) \]
\[ 4y + 2 = 20 - 5y \]

Now, we will move all terms involving \( y \) to one side and constant terms to the other:
\[ 4y + 5y = 20 - 2 \]
\[ 9y = 18 \]

Finally, divide both sides by 9:
\[ y = \frac{18}{9} \]
\[ y = 2 \]

Thus, the ordinate (y-coordinate) is 2.

### Step 3: Write the coordinates
Now that we have both coordinates, the point is:
\[ (-2, 2) \]

### Final Answer:
The coordinates of the point are \((-2, 2)\).

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