Suppose that x = 2-t and y = 4t+7.

a. If x=7, what is y?
b. If x=-3, what is y?
c. Find y in terms of x.

I don't know how to solve this, since x and y are in different equations. Could you please walk me through it?

Thanks!

I automatically did the last quesion but you are probably supposed to figure it out the hard way step by step:

When x = 7
7 = 2 - t
so t = 2 - 7 = -5
then
y = 4 t + 7
y = 4(-5) + 7
y = -20 + 7
y = -13
Now I would have just said:
y = 15 - 4x
y = 15 -4*7
y = 15 - 28
y = -13 again
Now you can do it for x = -3

Thanks!

is x=-3 then you plug it in to the first one and you get -3=2-t which is t=5 and then you plug 5 into the t in the equation y = 4t+7 and you get the answer which is y=27.

Certainly! I'll walk you through the process of solving these equations step by step.

First, let's start with the given equations:
x = 2 - t (Equation 1)
y = 4t + 7 (Equation 2)

a. If x = 7, what is y?
To find the value of y when x is equal to 7, we'll substitute x = 7 into Equation 1 and solve for t, and then substitute the value of t into Equation 2 to find y.

Substituting x = 7 into Equation 1:
7 = 2 - t

Next, we'll isolate t by subtracting 2 from both sides:
7 - 2 = -t
5 = -t

To get the value of t, we'll multiply both sides by -1:
-5 = t

Now that we have the value of t, we can substitute it into Equation 2 to find y:
y = 4t + 7
y = 4(-5) + 7
y = -20 + 7
y = -13

So, when x is equal to 7, y will be -13.

b. If x = -3, what is y?
We can follow a similar process to find the value of y when x is equal to -3.

Substituting x = -3 into Equation 1:
-3 = 2 - t

Isolating t by subtracting 2 from both sides:
-3 - 2 = -t
-5 = -t

Multiplying both sides by -1 to find the value of t:
5 = t

Now, substitute the value of t into Equation 2 to find y:
y = 4t + 7
y = 4(5) + 7
y = 20 + 7
y = 27

So, when x is equal to -3, y will be 27.

c. Find y in terms of x.
To find y in terms of x, we need to eliminate t from the equations. We can do this by substituting the value of x from Equation 1 into Equation 2.

Substituting x = 2 - t into Equation 2:
y = 4t + 7
y = 4(2 - x) + 7

Simplifying the equation:
y = 8 - 4x + 7
y = -4x + 15

Therefore, y in terms of x is given by the equation y = -4x + 15.

I hope this explanation helps! Let me know if you have any further questions.

t = 2 - x from the first equation

so
y = 4 (2-x) + 7
y = 8 - 4 x + 7
y = 15 - 4 x
You can do it now.