I had these problems on my test and for some reason got them wrong. Here are the problems:

Solve:
x-y=9
x+y=1

The test states that the answer is (5,-4)

I've checked ,y work and used substitution to solve this and still get x=4, y=-5.

The second problem is:
Solve the system of equations by graphing.
a=1/2b+5
a-4b=-2

The answer is (6,2)

Again i got the reverse of this; (2,6).

I have been at these for several hours and want to pull my hair out. Are my answers really wrong or is it the test? HELP!

Thanks

x-y=9

x+y=1

The test states that the answer is (5,-4)

I've checked ,y work and used substitution to solve this and still get x=4, y=-5.
------------------------
Check your answer
4 - -5 = 9 yes
4 + -5 = -1, not +1 wrong
Now adding the two equations
2 x = 10
x = 5
then
5+y = 1
y = -4

a=1/2b+5

a-4b=-2

substitute (1/2) b + 5 for a

(1/2) b + 5 - 4 b = -2

b + 10 - 8b = -4

-7 b = -14
b = 2
then
a = 1 + 5 = 6

It can be frustrating when you don't get the expected results on tests. Let's go through each problem step by step and see if we can figure out what went wrong.

Problem 1: Solve the system of equations using the method of substitution.
Equations:
1) x - y = 9
2) x + y = 1

First, we can solve equation 2) for x:
x = 1 - y

Next, we substitute this value of x into equation 1):
(1 - y) - y = 9
1 - 2y = 9
-2y = 9 - 1
-2y = 8
y = 8 / -2
y = -4

Now that we have the value of y, we can substitute it back into equation 2) to find x:
x + (-4) = 1
x - 4 = 1
x = 1 + 4
x = 5

So, the solution to the system of equations is x = 5 and y = -4.

Your answer, x = 4 and y = -5, seems to be swapped. It's possible that you made a mistake when substituting the values back into the original equations. It's always a good idea to double-check your calculations to avoid errors.

Problem 2: Solve the system of equations by graphing.
Equations:
1) a = (1/2)b + 5
2) a - 4b = -2

To solve this system by graphing, we need to plot the two equations on a coordinate plane and see where they intersect, if they do.

For equation 1), let's rearrange it to solve for b:
b = 2(a - 5)

Now, we can plot points for equation 1). For simplicity, let's choose arbitrary values for a and find the corresponding b values. Let's use a = 0, 1, and 2:

When a = 0, b = 2(0 - 5) = -10. So, one point on the graph is (0, -10).
When a = 1, b = 2(1 - 5) = -8. So, another point is (1, -8).
When a = 2, b = 2(2 - 5) = -6. So, another point is (2, -6).

Connect these points to form a line.

Next, let's rearrange equation 2) to solve for a:
a = 4b - 2

Again, let's choose arbitrary values for b and find the corresponding a values. Let's use b = 0, 1, and 2:

When b = 0, a = 4(0) - 2 = -2. So, one point on the graph is (-2, 0).
When b = 1, a = 4(1) - 2 = 2. So, another point is (2, 1).
When b = 2, a = 4(2) - 2 = 6. So, another point is (6, 2).

Connect these points to form a line.

If you graphed the two equations accurately, you should notice that the lines intersect at the point (6, 2). This means that (6, 2) is the solution to the system of equations.

Your answer, (2, 6), seems to have switched the coordinates. It's possible that when graphing, you accidentally switched the x and y coordinates, resulting in the wrong solution.

In both cases, it seems that there might have been a simple mix-up or calculation error. Always make sure to double-check your work, as even a small mistake can lead to different results.