Solve the following systems of equations using any method?

Question

a) y= -4x + 8 
5x + 3y = 3 


b) 4x - 4y = -3 
7x + 2y = 6

 

 

Answer 1

Substitution method :

a).

The system of equations are y = - 4x + 8 and 5x + 3y = 3.

Substitute the y = - 4x + 8 in 5x + 3y = 3 and solve for x.

5x + 3( - 4x + 8) = 3

5x - 12x + 24 = 3

- 7x = 3 - 24 = - 21

x = 21/7

⇒ x = 3.

Substitute the value x = 3 in y = - 4x + 8 and solve for y.

y = - 4(3) + 8

y = - 12 + 8

⇒ y = - 4.

The solution of the system is x = 3 and y = - 4.

b).

The system of equations are 4x - 4y = - 3 and 7x + 2y = 6.

Solve equation 4x - 4y = - 3 for y.

4y = 4x + 3

⇒ y = (4x + 3)/4.

Substitute the y = (4x + 3)/4 in 7x + 2y = 6 and solve for x.

7x + 2[ (4x + 3)/4 ] = 6

7x + [ (4x + 3)/2 ] = 6

14x + 4x + 3 = 12

18x = 12 - 3 = 9

⇒ x = 9/18 = 1/2.

Substitute the value x = 1/2 in y = (4x + 3)/4 and solve for y.

y = (4(1/2) + 3)/4

y = (2 + 3)/4

⇒ y = 5/4.

The solution of the system is x = 1/2 and y = 5/4.