# How do solve the following linear system?:  7x+3y=27 , 3x – 4y = 7 ?

Dec 28, 2015

$x = \frac{129}{37} , y = \frac{64}{70}$

#### Explanation:

the simplest way of answering this problem is by elimination of a variable.
1. Make the coefficient of any one of the variables same by multiplying the equations with respective constants
2. Adding or subtracting them to eliminate that variable from the equation.
3. Find the value of one variable from the new equation
4. Substitute value of this variable in one of the two original equations to get the second variable

In this case,
$7 x + 3 y = 27 , 3 x - 4 y = 7$
multiply first equation by 4 and second by 3
$28 x + 12 y = 108 , 9 x - 12 y = 21$
add these two equations to eliminate y
$28 x + 12 y = 108$ + $9 x - 12 y = 21$
$37 x = 129$
$x = \frac{129}{37}$
Now substitute this value into second equation
$3 x - 4 y = 7$
$3 \cdot \frac{129}{37} - 4 y = 7$
$4 y = 3 \cdot \frac{129}{37} - 7$
$y = \frac{64}{70}$