Question

What is the solution to this system of equations?

Answer 1

The solution is $x = \frac{-29}{13}, y = \frac{69}{26}$

Solution:

Given system of equations are:

4x + 6y = 7 --------- eqn 1

3x - 2y = -12 -------- eqn 2

Let us solve the system of equations by elimination method

Multiply eqn 2 by 3

9x - 6y = -36 ----- eqn 3

Add eqn 1 and eqn 3

4x + 6y = 7

9x - 6y = -36

( + ) --------------

13x = -29

$x = \frac{-29}{13}$

Substitute $x = \frac{-29}{13}$ in eqn 1

$4( \frac{-29}{13}) + 6y = 7\\\\6y = 7 + \frac{4 \times 29}{13}\\\\6y = \frac{207}{13}\\\\y = \frac{69}{26}$

Thus the solution is $x = \frac{-29}{13}, y = \frac{69}{26}$