Solve the system:
2.5(x−3y)−3=−3x+0.5 3(x+6y)+4=9y+19

The value of x and y that satisfy the equations is x = 2 and y = 1

Step-by-step explanation:

Given

2.5(x−3y)−3=−3x+0.5

3(x+6y)+4=9y+19

Required.

Find x and y

We start by opening all brackets

2.5(x−3y)−3=−3x+0.5 becomes

2.5x - 7.5y - 3 = -3x + 0.5

Collect like terms

2.5x + 3x - 7.5y = 3 + 0.5

5.5x - 7.5y = 3.5 Equation 1

In similar vein, 3(x+6y)+4=9y+19 becomes

3x + 18y + 4 = 9y + 19

Collect like terms

3x + 18y - 9y = 19 - 4

3x + 9y = 15

Multiply through by ⅓

⅓ * 3x + ⅓ * 9y = ⅓ * 15

x + 3y = 5

Make x the subject of formula

x = 5 - 3y

Substitute 5 - 3y for x in equation 1

5.5(5 - 3y) - 7.5y = 3.5

27.5 - 16.5y - 7.5y = 3.5

27.5 - 24y = 3.5

Collect like terms

-24y = 3.5 - 27.5

-24y = -24

Divide through by - 24

y = 1

Recall that x = 5 - 3y.

Substitute 1 for y in this equation

x = 5 - 3(1)

x = 5 - 3

x = 2

Hence, x = 2 and y = 1