Question

Solve the system by the method of substitution.

1.5x + 0.8y = 2.3
0.3x − 0.2y = 0.1

Answer 1

`\boxed{\sf \ \ \ x = 1 \ \ , \ \ y = 1 \ \ \ }`

Explanation:

hello

we can multiply by 10 both parts of the equations so this is equivalent to

(1) 15x + 8y = 23

(2) 3x - 2y = 1

and we are asked to use the method of substitution

from (2) we can write 3x = 2y + 1

and we substitute 3x in (1) as 15x = 5*3x it comes

5*(2y+1) + 8y = 23

<=> 10y + 5 + 8y = 23

<=> 18y + 5 = 23 let's subtract 5

<=> 18y = 23 - 5 = 18 let's divide by 18

<=> y = 1

and finally replace y in 3x = 2y + 1

3x = 2*1 + 1 = 3 <=> x = 1 (divide by 3)

so the solution is x = 1, y = 1

hope this helps

Answer 2

(1,1)

Explanation:

1.5x + 0.8y = 2.3

0.3x − 0.2y = 0.1

I'm going to multiply both of these equations by 10, so we can work with whole numbers.

15x+8y=23

3x-2y=1

We can simplify one of the equations to isolate a variable.

I'm going to isolate y in equation 2.

3x-2y=1

Subtract 3x from both sides.

-2y=-3x+1

Divide both sides by -2.

y=1.5x-0.5

Plug 1.5x-0.5 into the first equation for y.

15x+8(1.5x-0.5)=23

Distribute.

15x+12x-4=23

Combine like terms.

27x-4=23

Add 4 to both sides.

27x=27

Divide both sides by 27.

x=1

Plug that back into original equation to find y.

15(1)+8y=23

15+8y=23

Subtract 15 from both sides.

8y=8

Divide both sides by 8.

y=1

The solution to the system is (1,1).