Find the co-ordinates of the point whose abscissa is the solution of the first quadrant and the ordinate is the solution of the second equation.
`0.5x-3=-0.25x` and `8-0.2(y+3)=3y+1`

Answer

To find the coordinates of the point whose abscissa is the solution of the first equation and the 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:
\[ 0.5x - 3 = -0.25x \]

**Hint:** Start by isolating x on one side of the equation.

1. Add \( 0.25x \) to both sides:
\[ 0.5x + 0.25x - 3 = 0 \]
\[ 0.75x - 3 = 0 \]

2. Add 3 to both sides:
\[ 0.75x = 3 \]

3. Divide both sides by 0.75:
\[ x = \frac{3}{0.75} \]
\[ x = 4 \]

### Step 2: Solve the second equation for y
The second equation is:
\[ 8 - 0.2(y + 3) = 3y + 1 \]

**Hint:** Distribute and rearrange the equation to isolate y.

1. Distribute \( -0.2 \):
\[ 8 - 0.2y - 0.6 = 3y + 1 \]
\[ 7.4 - 0.2y = 3y + 1 \]

2. Move \( 3y \) to the left side:
\[ 7.4 - 1 = 3y + 0.2y \]
\[ 6.4 = 3.2y \]

3. Divide both sides by 3.2:
\[ y = \frac{6.4}{3.2} \]
\[ y = 2 \]

### Step 3: Combine the results
Now that we have the values of x and y:
- Abscissa (x) = 4
- Ordinate (y) = 2

Thus, the coordinates of the point are:
\[ (4, 2) \]

### Final Answer:
The coordinates of the point are \( (4, 2) \).

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