Answer:
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 [tex]c\cdot a =c\cdot b[/tex]
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];
[tex]\frac{31a}{31} =\frac{217}{31}[/tex]
Simplify:
a = 7
By substitution property of equality, substitute the value of a =7 in equation [1];
[tex]2(7)+7b =0[/tex]
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]
[tex]\frac{7b}{7} =\frac{-14}{7}[/tex]
Simplify:
b = -2
