Question

Solve each of the following pairs of equation by tha eliminations method
1. 8x+ 5y = 9
3x+2y = 4​

Answer 1

Answer:

here's your detailed answer..

Answer 2

Step-by-step explanation:

x = -2 and y = 5

Step-by-step explanation:

Given Equations are,

8x + 5y = 9

8x + 5y - 9 = 0 ....................(1)

3x + 2y = 4

3x + 2y - 4 = 0 .......................(2)

here,

a_1=8\:,\:b_1=5\:,\:c_1=-9\:,\:a_2=3\:,\:b_2=2\:and\:c_2=-4a

1

=8,b

1

=5,c

1

=−9,a

2

=3,b

2

=2andc

2

=−4

since, \frac{a_1}{a_2}\neq\frac{a_2}{b_2}

a

2

a

1



=

b

2

a

2

There exist unique solution,

By cross multiplication method we get,

\frac{x}{5\times(-4)-2\times(-9)}=\frac{y}{-9\times3-(-4)\times8}=\frac{1}{8\times2-3\times5}

5×(−4)−2×(−9)

x

=

−9×3−(−4)×8

y

=

8×2−3×5

1

First Consider,

\frac{x}{5\times(-4)-2\times(-9)}=\frac{1}{8\times2-3\times5}

5×(−4)−2×(−9)

x

=

8×2−3×5

1

\frac{x}{-2}=\frac{1}{1}

−2

x

=

1

1

x=-2x=−2

Secondly consider,

\frac{y}{-9\times3-(-4)\times8}=\frac{1}{8\times2-3\times5}

−9×3−(−4)×8

y

=

8×2−3×5

1

\frac{y}{5}=\frac{1}{1}

5

y

=

1

1

y=5y=5

Therefore, x = -2 and y = 5