To solve this problem, you must plug 109.95 and 151.95 into the equation for C.

109.95 = .25*(t-500)+70.95

109.95-70.95 = .25*t-.25*500

39 = .25*t-125

.25*t = 39+125

t = 164 / .25

t= 656.

Using the same algebraic manipulation, plug 151.95 for C into the equation and solve for t.

151.95 = .25*(t-500)+70.95

t = 824.

Answer is between t = 656 and t = 824.

Personally I think that matrices are the easiest way to solve 2 equations. If you know how to put a matrix into your calculator, it makes the process very simple.

[ .3 −.2.5 .3 ]^(-1) * (

4−717

¿

Answer = (5.8824, -11.1765) when solving the matrix.

To use elimination, you could multiply the top equation by 3 and the bottom by 2.

.9x -.6y = 12

1x+.6y= -14/17

Now if you add these two equations together, you can cancel the y variables.

1.9x+0*y = 190/17

X = ( 19017 )1.9

= 5.8824

Now plug x into either equation and solve for y.

.3*(5.8824)-.2*y = 4

1.7647-.2*y = 4

-.2*y = 2.2353

Y = 2.2353 / -.2 = -11.1765

Consistent because there is at least one solution.

The equations are dependent, both the lines from the two graphs are overlayed upon each other.

Using a matrix, the solution is x = 3 and y = -9. You can obtain the answer by multiplying the top equation by -8 and summing the two equations like this:

-48*x-8*y=-72

7*x+8*y = -51

Sum the two equations: -41*x+0*y = -123, x = -123/-41 = 3.

Now plug x=3 into either the top or bottom equation. You will get y = -9.

Answer as an ordered pair is (3,-9).

Since there is a solution, the system of equations is consistent.

The system represents the graph in C because you can see them intersect at 3,-9.

They want you to plug x = 8 and y = 20 into the equality and see if it’s true.

3*(20)-4*(8) > 7?

60-32> 7?

28 > 7?

Is 28 greater than 7?

Yes the pair is a solution.

The rule of thumb here is this: If you have greater or less than, the data point will be “open” (which means it is represented by a parenthesis in this case).

If you have a “greater than or equal to” or a “less than or equal to” sign, then the data point will be “closed” (which means it is represented by the bracket in this case).

So your answer would be C because it is between 0 and 16, yet it does not include 0 and 16.

Solve this just like any other equation.

a+4 ≤ -17

a≤-21

So your answer would be B because it is less than -21 and it includes -21.

You can solve this any method you like even though they say to solve by substitution.

Multiply the bottom by 3.

-9*x+3*y = 42

9*x + 9*y =54

Add the two equations together and solve for y.

0*x+12*y = 96

Y = 96/12 = 8.

Now plug y = 8 into either equation and solve for x.

-3*x+(8) = 14

-3*x = 6

x= -2

(-2,8) is your final answer.

4 y−3<7 y−4

4 y−3+4<7 y

4 y+1<7 y

1<3 y

13< y

y> 13

Is the final answer.

Plug the numbers they give you in for x and see if they make the equation true.

-6-1 ≥6?

-7 ≥6? No .

3-1≥6? No .

6-1≥6?

5≥6? No .

17-1≥6?Yes .

X+6←4

X←10

For the second equation:

x+6>4

x>-2

Since B is the only one that represents a number less than -10 and greater than -2, that is the answer, B.

*Notice that if the solution was x ≤−10∧x≥−2 ,thenCwould be your answer .

Same as last problem, just solve the two equations separately.

4x+18≥14

4x ≥−4

X≥−1

2x-18≥−14

2x≥4

X≥2

Since X is greater than or equal to -1, you second equation is meaningless.

The answer is B.

If you take the determinant of the system of equations:

5*7- (-7*-5) = 0.

If the determinant of a system of equations is zero, it means there are no solutions.

The equations are inconsistent because there are no solutions.

The graph would be A because the two lines do not intersect.

3*[5m-(m+4)] simplifies to 3*[5m-m-4], which simplifies to 3*[4m-4] = 12m-12

-4(m-6) simplifies to -4m+24.

12m-12¿−4m+24

16m¿36

m¿ 3616

m¿ 94

6y≤−5 x+30

y≤−56x+5

Create a data point at 5.

Go vertical by -5 (down) and go horizontal (right) by 6, that is your slope.

Create another data point by going vertical (up) 5 and going horizontal (left) by 6.

Since y is less than all those values, your y should be shaded on the bottom of the graph but will include the line.

I skipped this one to leave as an exercise for you. Solve all the equations for y and plot them using standard y = mx+b notation. The equation x ≥0 just means that you are only using values from the middle of the graph (x=0) all the way to the far right of the graph (x=∞ ¿

I’ll just put this in a matrix, you can solve this any way you like.

(-5/29, -176/29)

.16*x+.08*y = .1*320.

x+y = 320

Solve the two equations.

80 lbs of soybean and 240 lbs of cornmeal.

Because there is no “greater/less than or equal to”’s, the notation will only be in parenthesis.

The answer is B.

5*x/4 – 1/8 – 5/3 < 1/3

5x/4 – 3/24-40/24 < 8/24

5x/4 -43/24 < 8/24

5x/4 < 51/24

5x < (51/24)*4 = 5x < 204/24.

X < 204 / (120)

X<17/10

2x+2y = 128

X = 7+2*y

Solve the two equations.

Length = 45

Width = 19

9600/.8 = 12000

So the answer is D, greater than or equal to 12,000.

Graph 1 corresponds to y+x≤3

Graph 2 corresponds to 3x≥5 y−15

Graph 3 corresponds to 2x-3y<6

2x+2y = 206

Y = x+33

Solve the two equations.

Width = 35

Length = 68