Question

Solve the system of equations: -5x+2y=1 -8x+9y=19 X=? Y=?

Answer 1

Answer:

X = 1

Y = 3

Step-by-step explanation:

Given equations are;

-5x+2y=1              Eqn 1

-8x+9y=19          Eqn 2

Multiplying Eqn 1 by -8

-8(-5x+2y=1)

40x - 16y = -8     Eqn 3

Multiplying Eqn 2 by 5

5(-8x+9y=19)

-40x+45y=95     Eqn 4

Adding Eqn 3 and 4

40x - 16y - 40x + 45y = 95 - 8

29y = 87

Dividing both sides by 29

$\frac{29y}{29}=\frac{87}{29}\\y = 3$

Putting y = 3 in Eqn 1

-5x + 2(3) = 1

-5x + 6 = 1

-5x = 1 - 6

-5x = -5

x = 1

Hence,

X = 1

Y = 3

Answer 2

2y=1+5x (moving 5x to the other side) {equation 1}

Y= (1+5x)/2 (dividing both sides by 2)

Substitute {Y=(1+5x)/2} into equation: (-8x+9y=19)

Therefore giving you:

-8x+9(1+5x)/2=19

-8x+(9+45x)/2=19

(multiply through by 2 to remove the fraction)

-16x+9+45x=38

45x-16x=38-9(grouping like terms)

29x=29

Divide both sides by 29

X=1

Substitute X=1 into equation (-5x+2y=1)

-5(1)+2y=1

(-5)+2y=1

2y=1+5

2y=6

2y/2=6/2 (dividing both sides by 2)

Y=3.

:X=1 and Y=3