How do you solve the system #x = y + 4# and #2x - 5y = 2# by substitution?

Answer 1
#x = y + 4#————(1) #2x - 5y = 2#————— (2)
The following results from entering #x# into the second equation:
#2(y+4) - 5y = 2#

$2y+8 - 5y = 2#

# -3y + 8 = 2#
#-3y = 2–8#
#-3y = -6#
When we divide both sides by #-3#, we obtain:
(-6)/-3# = #(cancel(-3)y)/cancel(-3)
#color(y = 2#) for green
The following results from changing #y=2# in the first equation:
#x equals 2 + 4#

Green #color (x = 6)

The answers to the following two equations are: #x = 6; y = 2#

Confirm:

Replace #x and y# with their respective values in each equation to check if they are satisfied.
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Answer 2

To solve the system (x = y + 4) and (2x - 5y = 2) by substitution:

  1. Solve the first equation for one variable (let's solve for (x)): (x = y + 4).
  2. Substitute the expression for (x) from the first equation into the second equation.
  3. Solve the resulting equation for the variable left.

Here's the process:

(2x - 5y = 2) (Given second equation)

Substitute (x = y + 4) into the second equation:

(2(y + 4) - 5y = 2)

Now, solve for (y):

(2y + 8 - 5y = 2)

(-3y + 8 = 2)

(-3y = -6)

(y = 2)

Now that we have found (y), substitute this value back into either of the original equations to find (x). Let's use the first equation:

(x = y + 4)

(x = 2 + 4)

(x = 6)

So, the solution to the system is (x = 6) and (y = 2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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