The equations 2 x minus y = negative 2, 3 x + 2 y = 5, 4 x minus y = 2, and 22 x + 10 y = 7 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, 2.5) and (1.75, 0). Blue line goes through (0.5, 0) and (1, 2). Pink line goes through (negative 1, 0), and (0, 2). Purple line goes through (negative 0.75, 2.5) and (0, 0.75). Which system of equations has a solution of approximately (–0.3, 1.4)? 2 x minus y = negative 2 and 22 x + 10 y = 7 3 x + 2 y = 5 and 4 x minus y = 2 4 x minus y = 2 and 22 x + 10 y = 7 2 x minus y = negative 2 and 3 x + 2 y = 5

2 x - y = - 2 and 22 x + 10 y = 7

Step-by-step explanation:

To find the equation to produce a solution of approximately (–0.3, 1.4), we have to solve the equations simultaneously.

a) For line 2 x - y = - 2 and 22 x + 10 y = 7

Multiply line 1 by 10 to give : 20x - 10y = -20

Add 20x - 10y = -20 and 22 x + 10 y = 7 to get:

42x = -13

x = -13/42 = -0.3

Put x = -0.3 in 2 x - y = - 2  to get:

2(-0.3) - y = - 2

-0.6 - y = -2

y = 2 - 0.6 = 1.4

x = - 0.3 and y = 1.4

This is the correct option

b) For line 3 x + 2 y = 5 and 4 x - y = 2

Multiply line 2 by 2 to give : 8x - 2y = 8

Add 8x - 2y = 48 and 3 x + 2 y = 5 to get:

11x = 13

x = 13/11 = 1.2

Put x = 1.2 in 3 x + 2 y = 5  to get:

3 (1.2) + 2 y = 5

y = 1.4

x = 1.2 and y = 1.4

c)  For line 4 x - y =  2 and 22 x + 10 y = 7

Multiply line 1 by 10 to give : 40x - 10y = 20

Add 40x - 10y = 20 and 22 x + 10 y = 7 to get:

62x = 27

x = 0.44

Put x = 0.44 in 4x - y =  2  to get:

y = -0.24

d) For line 2 x - y = - 2 and 3 x + 2 y = 5

Multiply line 1 by 2 to give : 4x - 2y = -4

Add 4x - 2y = -4 and 3x + 2 y = 5 to get:

7x = 1

x = 0.14

Put x = 0.14 in 2 x - y = - 2  to get:

y = 2.28