Question

Which properties justify the steps taken to solve the system?

{2a+7b=0
{3a−5b=31

Drag the answers into the boxes to match each step.

Answer 1

Given the system:

2a+7b=0 ......[1]

3a-5b=31 ......[2]

Multiplication property of equality states that you multiply the same number to both sides of an equation.

i,e if a=b then
`c\cdot a =c\cdot b`

Multiply by 5 to both sides in equation [1] we get;

10a+35b=0 ......[3]

Also, multiply by 7 to both sides in equation [2] we get;

21a-35b=217 ......[4]

Addition property of equality states that allows one to add the same quantity to both sides of an equation.

Adding the equation [3] and [4] we get;

10a+35b+21a-35b =0+217

Simplify:

31a =217 ......[5]

Division property of equality states that you divide the same number to both sides of an equation

Divide by 31 to both sides of an equation [5];

`(31a)/(31) =(217)/(31)`

Simplify:

a = 7

By substitution property of equality, substitute the value of a =7 in equation [1];

`2(7)+7b =0`

Simplify:

14+7b =0 ......[6]

Subtraction Property of Equality states that you subtract the same number from both sides of an equation.

Subtract 14 from both sides of an equation in [6];

14+7b-14=0-14

Simplify:

7b=-14 ......[7]

By Division Property of Equality;

Divide by 7 to both sides of an equation in [7]

`(7b)/(7) =(-14)/(7)`

Simplify:

b = -2