Question

Solve the following simultaneous equations by the substitution method.

0.4x + 0.5y = 2.5, 0.3x – 0.1y = 1.4

Answer 1

Given the simultaneous equations:

0.4x + 0.5y = 2.5

0.3x – 0.1y = 1.4

Step 1: Express (x) from equation (2)

From (2),

0.3x – 0.1y = 1.4 

0.3x = 1.4 + 0.1y 

`x = (1.4 + 0.1y)/0.3`

`x = 1.4/0.3 + (0.1y)/0.3`

`x = 14/3 + y/3`

Step 2: Substitute this value of (x) into equation (1)

Substitute `(x = 14/3 + y/3)` into (1):

`0.4 (14/3 + y/3) + 0.5 y = 2.5`

Multiply out:

`0.4 xx 14/3 + 0.4 xx y/3 + 0.5 y = 2.5` 

`(5.6)/(3) + (0.4y)/(3) + 0.5 y = 2.5`

Convert fractions to decimals for clarity:

1.8667 + 0.1333y + 0.5y = 2.5 

1.8667 + 0.6333y = 2.5

Step 3: Solve for (y)

0.6333y = 2.5 – 1.8667

0.6333y = 0.6333 

`y = (0.6333)/(0.6333)`

y = 1

Step 4: Substitute (y = 1) back to find (x)

`x = 14/3 + 1/3`

`x = 15/3`

x = 5