Need some help with this problems please.?

Question

Hello everyone, need some help with some math exercises.

1-) Which ordered pair is a solution to the system?
-2x+7y=31
5x-11y=-45
I answered (2,5)

2-) Solve the system using the graphing method.
x+y=8
3x+y=20
I answered No Solution

3-) Solve the system using the substitution method.
y=5x+7
-3y+15x=-8
I got (7,-8)

4-) Solve the equations using the most convenient method.
8x-4y=6
16x=8y+12
Got ( 8,4 )

5-) If z(t)=2t.square+7t-4, find z(-1) and z(2)
This one im stumped.

Thanks for the help.

Answer 1

You got the first one correct, the others are incorrect.

1) Correct -- If you just plug in x=2, y=5, both equations will be satisfied, so you did this correctly. Always double-check your answers.

2) Incorrect -- x = 6, y = 2 is the answer, so 'No Solution' is incorrect.

To graph this, first put them all in terms of y.
y = -x + 8
y = -3x + 20

The first line goes through the y intercept of 8 and downward with a slope of -1.
(0, 8), (1, 7), (2, 6), (3, 5), (4, 4), (5,3), (6, 2)...
The second line goes through through the y intercept of 20 and downward with a slope of -3.
(0, 20), (1, 17), (2, 14), (3, 11), (4, 8), (5, 5), (6, 2)...

If you look at the numbers and draw this accurately, you'll definitely see that they cross at (6, 2).

3) Incorrect -- Double-check your answer; it won't satisfy both equations.

The first equation is already in terms of y, so just substitute that into the second equation:
y = 5x + 7
-3 (5x + 7) + 15x = -8
-15x - 21 + 15x = -8

The x terms cancel out and you have
-21 = -8

Given that you have come to a contradiction this tells you that there are *no solutions*.

4) Incorrect -- These two are exactly the same function (just multiplied by 2), so there are an infinite number of solutions. The functions are essentially the same line where every point will be on the other line.

5) Just substitute t = -1 to get your answer. Do the same for t = 2.

z(t) = 2t² + 7t - 4
z(-1) = 2(-1)² + 7(-1) - 4
z(-1) = 2(1) + (-7) - 4
z(-1) = 2 - 7 - 4
z(-1) = -9

z(2) = 2(2)² + 7(2) - 4
z(2) = 2(4) + 14 - 4
z(2) = 8 + 10
z(2) = 18

Answer 2

i can help....
(1) correct

(2) solution is (6, 2) - try graphing it on a graph paper and using ruler. pay close attention to the slopes.

(3) these two are parallel lines so there is no solution
i.e. -3(5x + 7) + 15x = -8
so you get -21 = -8

(4) these two lines are the same so they share every single ordered pair, i.e. there are infinitely many solutions

(5) z(t) only indicates that z is a function in terms of t. so find z(-1) and z(2) all you need to do is substitute -1 for t, and 2 for t.

hope it helps!

Answer 3

Problem 2 has a solution. Write the first equation under the second to get

3x + y = 20
x + y = 8 and now subtract second from first to get

2x = 12 so x = 6 so substitute x=6 in second

6 + y = 8 so y = 2.

Solution (6,2)

Answer 4

1) is correct
2) should be (6, 2)
3) should be No Solution
4) these equations are equivalent, so there are infinite solutions.
5) z(-1) = -9 and z(2) = 18 (plug each # in for t in the equation)

Answer 5

2 has a solution.
3 and 4 no solution
5)z(t)=2t^2+7t-4
z(-1)=2(-1)^2+7(-1)-4
2-7-4
=-9
z(2)=2(2^2)+7(2)-4
=8+14-4
=18

3) y=5x+7
-3(5x+7)+15x=-8
-15x-21+15x=-8
-21=-8 no solution for x

2)y=8-x
3x+(8-x)=20
2x+8=20
2x=12
x=6
y=2 has a solution