Questions: Use the substitution method to solve the system 9x - 3y = 12 y + 6 = 2x

Use the substitution method to solve the system 9x - 3y = 12 y + 6 = 2x
Transcript text: Use the substitution method to solve the system \[ \begin{array}{l} 9 x-3 y=12 \\ y+6=2 x \end{array} \]
failed

Solution

failed
failed

Solution Steps

To solve the system of equations using the substitution method, follow these steps:

  1. Solve one of the equations for one variable in terms of the other variable.
  2. Substitute this expression into the other equation.
  3. Solve the resulting equation for the single variable.
  4. Substitute back to find the value of the other variable.
Step 1: Solve the Second Equation for \( y \)

Given the system of equations: \[ \begin{array}{l} 9x - 3y = 12 \\ y + 6 = 2x \end{array} \]

First, solve the second equation for \( y \): \[ y + 6 = 2x \implies y = 2x - 6 \]

Step 2: Substitute \( y \) into the First Equation

Substitute \( y = 2x - 6 \) into the first equation: \[ 9x - 3(2x - 6) = 12 \]

Simplify the equation: \[ 9x - 6x + 18 = 12 \implies 3x + 18 = 12 \]

Step 3: Solve for \( x \)

Solve the simplified equation for \( x \): \[ 3x + 18 = 12 \implies 3x = 12 - 18 \implies 3x = -6 \implies x = -2 \]

Step 4: Substitute \( x \) back into the Expression for \( y \)

Substitute \( x = -2 \) back into the expression \( y = 2x - 6 \): \[ y = 2(-2) - 6 = -4 - 6 = -10 \]

Final Answer

\(\boxed{(x, y) = \left(-2, -10\right)}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
In the braces below, list all subsets of the set 6,5,4. Write each subset in your list in roster form. If there is more than one subset in your list, separate them with commas. If you need the empty set in your list, use the symbol ∅.
failedAnswered
It is estimated that in the overall population, around 1 in every 10 100 1,000 100,000
failedAnswered
Crossbracing is acceptable as a midrail when the crossing point is between inches and inches above the work platform.
failedAnswered
Lengthwise, long bone growth during infancy and youth is exclusively through - interstitial growth of the epiphyseal plates - the secretion of bone matrix into the medullary cavity - calcification of the matrix of the zone underlying articular cartilage - differentiation of osteoclasts into osteocytes
failedAnswered
Example 4 Suppose M is the midpoint of FG. Find each missing 34. FM=5y+13, MG=5-3y, FG=? 35. FM