If each of the following find the co -ordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation:
`(2a)/3-1=a/2,(15-4b)/7=(2b-1)/3`

Answer

To solve the problem, we need 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.

### Step 1: Solve the first equation
The first equation is given as:
\[ \frac{2a}{3} - 1 = \frac{a}{2} \]

**Hint:** Start by isolating the variable \(a\).

1. Add 1 to both sides:
\[ \frac{2a}{3} = \frac{a}{2} + 1 \]

2. To eliminate the fractions, find a common denominator. The least common multiple of 3 and 2 is 6. Multiply every term by 6:
\[ 6 \cdot \frac{2a}{3} = 6 \cdot \frac{a}{2} + 6 \cdot 1 \]
This simplifies to:
\[ 4a = 3a + 6 \]

3. Now, subtract \(3a\) from both sides:
\[ 4a - 3a = 6 \]
Which simplifies to:
\[ a = 6 \]

### Step 2: Solve the second equation
The second equation is given as:
\[ \frac{15 - 4b}{7} = \frac{2b - 1}{3} \]

**Hint:** Use cross-multiplication to eliminate the fractions.

1. Cross-multiply:
\[ 3(15 - 4b) = 7(2b - 1) \]

2. Distribute both sides:
\[ 45 - 12b = 14b - 7 \]

3. Now, add \(12b\) to both sides:
\[ 45 = 14b + 12b - 7 \]
Which simplifies to:
\[ 45 = 26b - 7 \]

4. Add 7 to both sides:
\[ 45 + 7 = 26b \]
This gives:
\[ 52 = 26b \]

5. Finally, divide by 26:
\[ b = 2 \]

### Step 3: Find the coordinates
Now we have the values:
- \(a = 6\) (abscissa)
- \(b = 2\) (ordinate)

Thus, the coordinates of the point are:
\[ (6, 2) \]

### Summary
The coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation are \((6, 2)\).

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