Which statement is true about the following system of equations? 3x - 1/2y = 1
x + 2y = 7
Select one:
a. y<x
O b. y=x
O c. y>x
d. can not be determined

c. y>x

Step-by-step explanation:

When given a system of equations, one of many methods can be used to solve these types of systems. One of these includes substitution which involves solving for one variable that is included in another equation, and putting that equality in place of the variable.

Here is what I mean by this:

Given that 3x - 1/2y = 1, and x + 2y = 7, you can rearrange the x + 2y = 7 to solve for x by isolating it.

x + 2y = 7 → x = 2y - 2y = 7 - 2y [for an equation, what you do to one side, you must do to the other] → x = 7 - 2y.

Now that we have an expression which is equal to x.

We can directly replace that with the 3x in the other equation by multypling this by 3:

x = 7 - 2y → 3(x) - 1/2y = 1

3(7 - 2y) - 1/2y = 1

Now that we only have y's, we can simply the equation, and solve for y.

21 - 6y - 1/2y = 1

21 -13/2y = 1

(get rid of the constant on the left side by subtracting)

-21 -21

-13/2y = -20

(remove the denominator by Multiplying)

×2 ×2

-13y = -40

÷13 ÷13

(cancel out the coefficient by dividing)

-y = -40/13

(take the opposite of the other side to make y positive)

×-1 ×-1

y = 40/13.

Now that we have y just solve for x since we already have a term of x in the other equation:

y = 40/13 → x + 2y = 7

x + 2(40/13) = 7

x + 80/13 = 7

Then subtract both constants to find x:

x + 80/13 - 80/13 = 7 - 80/13

x = 7 - 80/13

(create like denominators, but Multipy

it has the same slope and a different y-intercept

hope this : )

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.