Question

Solve the system of equations:

a) 6x - 9.4 = 1.7x - 1
b) 3.5 - 9a = 2(0.5a - 4)
c) 0.2(5x - 6) + 2x = 0.8
d) -3(y + 2.5) = 6.9 - 4.2y
e) 7(x - 8.2) = 3x + 19
f) 0.6y - 1.5 = 0.3(y - 4)

Answer 1

To solve the system of equations, isolate the variable by performing mathematical operations to both sides of the equation. Here are the step-by-step solutions for each equation.

Step-by-step explanation:

To solve the system of equations, we need to isolate the variable on one side of the equation. Here are the step-by-step solutions for each equation:

a) 6x - 9.4 = 1.7x - 1:

1. Subtract 1.7x from both sides: 6x - 1.7x - 9.4 = -1
2. Combine like terms: 4.3x - 9.4 = -1
3. Add 9.4 to both sides: 4.3x = 8.4
4. Divide by 4.3: x = 1.95

b) 3.5 - 9a = 2(0.5a - 4):

1. Distribute 2 to the terms inside the parentheses: 3.5 - 9a = a - 8
2. Add 9a to both sides: 3.5 = 10a - 8
3. Add 8 to both sides: 11.5 = 10a
4. Divide by 10: a = 1.15

c) 0.2(5x - 6) + 2x = 0.8:

1. Distribute 0.2 to the terms inside the parentheses: x - 1.2 + 2x = 0.8
2. Combine like terms: 3x - 1.2 = 0.8
3. Add 1.2 to both sides: 3x = 2
4. Divide by 3: x = 0.67

d) -3(y + 2.5) = 6.9 - 4.2y:

1. Distribute -3 to the terms inside the parentheses: -3y - 7.5 = 6.9 - 4.2y
2. Add 4.2y to both sides: -3y + 4.2y - 7.5 = 6.9
3. Combine like terms: 1.2y - 7.5 = 6.9
4. Add 7.5 to both sides: 1.2y = 14.4
5. Divide by 1.2: y = 12

e) 7(x - 8.2) = 3x + 19:

1. Distribute 7 to the terms inside the parentheses: 7x - 57.4 = 3x + 19
2. Subtract 3x from both sides: 7x - 3x - 57.4 = 19
3. Combine like terms: 4x - 57.4 = 19
4. Add 57.4 to both sides: 4x = 76.4
5. Divide by 4: x = 19.1

f) 0.6y - 1.5 = 0.3(y - 4):

1. Distribute 0.3 to the terms inside the parentheses: 0.6y - 1.5 = 0.3y - 1.2
2. Subtract 0.3y from both sides: 0.6y - 0.3y - 1.5 = -1.2
3. Combine like terms: 0.3y - 1.5 = -1.2
4. Add 1.5 to both sides: 0.3y = 0.3
5. Divide by 0.3: y = 1