Question

Solve by elimination method: 2x – 3y = 13; 7x – 2y = 20

Answer 1

Answer:

Step-by-step explanation:

2 x - 3 y = 13. Equation 1

7 x - 2 Y = 20. Equation 2

The LCM of 7 and 2 is 14

Therefore multiply equation 1 with 7 and equation 2 with 2

14x -21y =91

14 x - 4y 40

Subtract both the sides with each other

(14 x - 21 y) -( 14 x - 4y)=(91-40)

-18y=51

-y=51/18

y = -3

2x - 3 (- 3) = 13

2x+9 =13

2x =13-9

x=4/2

x=2

Answer 2

Answer:

By using the elimination method, the value of $x = 2 ; y = - 3$

Solution:

Given,  

$\begin{aligned} 2 x - 3 y & = 13 & \ldots \ldots ( i ) \\\\ 7 x - 2 y & = 20 \ldots & ( i i ) \end{aligned}$

Multiply equation (ii) by 3 and (i) by 2, we get

$\begin{array} { c } { ( i i ) \times 3 \Rightarrow 21 x - 6 y = 60 } \\\\ { ( i ) \times 2 \Rightarrow 4 x - 6 y = 26 } \end{array}$

Subtracting we get,  

$\begin{array} { c } { 17 x = 34 } \\\\ { x = \frac { 34 } { 17 } = 2 } \\\\ { x = 2 } \end{array}$

Putting x = 2 in equation (i), we get,

$\begin{array} { c } { 2 \times 2 - 3 y = 13 } \\\\ { 4 - 3 y = 13 } \\\\ { - 3 y = 13 - 4 } \\\\ { - 3 y = 9 } \\\\ { y = - \frac { 9 } { 3 } = - 3 } \\\\ { y = - 3 } \end{array}$

Thus, $x = 2 ; y = - 3$

By using the elimination method, the value of $x = 2 ; y = - 3$