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.

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

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];

Simplify:

a = 7

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

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]

Simplify:

b = -2

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

your question is incomplete, write all the numbers in the sequence that it tells you.  

step-by-step explanation: