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Complete steps 2 and 3 to solve the system of equations.

  y = 4x – 5,

y = –3

1. Use substitution to create a one-variable linear equation: –3 = 4x – 5.

2. Solve to determine the value of the unknown variable.

3. Write the solution to the system of equations as an ordered pair.

The solution to the system is (
, –3).

1 answer

Let's complete steps 2 and 3 to solve the system of equations.

Given:

  1. \( y = 4x - 5 \)
  2. \( y = -3 \)

You've already substituted \( y = -3 \) into the first equation:

Step 2: Solve to determine the value of the unknown variable.

Substituting gives us the equation:

\[ -3 = 4x - 5 \]

Now, add 5 to both sides:

\[ -3 + 5 = 4x \]

This simplifies to:

\[ 2 = 4x \]

Now, divide both sides by 4:

\[ x = \frac{2}{4} = \frac{1}{2} \]

Step 3: Write the solution to the system of equations as an ordered pair.

We found \( x = \frac{1}{2} \) and we know \( y = -3 \).

Thus, the solution to the system is:

\[ \left( \frac{1}{2}, -3 \right) \]

So, the final solution to the system is:

The solution to the system is \(\left( \frac{1}{2}, -3 \right)\).