Q1. The solution of pair of equations 2x-3y=1 and 4x-2y= 6, is
(1) (3, 1)
(3) (2,4)
(2) (2, 2)
(-1,2)

We are given the system of equations:

1. \( 2x - 3y = 1 \)
2. \( 4x - 2y = 6 \)

### Step 1: Solve using substitution or elimination
We'll use the **elimination method**. First, we'll multiply the first equation by 2 to align the coefficients of \( x \).

\[
2(2x - 3y) = 2(1) \implies 4x - 6y = 2
\]

Now, we subtract this from the second equation:

\[
(4x - 2y) - (4x - 6y) = 6 - 2
\]

This simplifies to:

\[
4y = 4 \implies y = 1
\]

### Step 2: Substitute \( y = 1 \) into one of the original equations
We'll substitute \( y = 1 \) into the first equation:

\[
2x - 3(1) = 1 \implies 2x - 3 = 1 \implies 2x = 4 \implies x = 2
\]

### Solution:
The solution is \( (x, y) = (2, 1) \).

Since this doesn't match any of the provided options, there may be a misprint in the choices. However, based on the solution, the answer is \( (2, 1) \).

Would you like further details or have any questions? Here are 5 related problems for practice:

1. Solve the system of equations: \( x + y = 4 \) and \( 2x - y = 3 \).
2. Solve the system: \( 3x - y = 7 \) and \( 2x + y = 4 \).
3. What is the solution to \( 5x + 2y = 12 \) and \( 3x - 4y = -2 \)?
4. Find the values of \( x \) and \( y \) for the equations \( 6x - y = 5 \) and \( 4x + y = 3 \).
5. Solve \( 3x + 4y = 10 \) and \( 2x - 5y = 1 \).

**Tip**: Always check the solution by substituting the values of \( x \) and \( y \) back into the original equations.

The solution of pair of equations 2x-3y=1 and 4x-2y=6, is (1) (3, 1) (2) (2, 2) (3) (2, 4) (-1, 2)

Learn how to solve the system of equations 2x-3y=1 and 4x-2y=6 using the elimination method. This step-by-step solution covers algebraic concepts such as solving linear equations through coefficient alignment and substitution. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation