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Find the solution to the system of equations, x + 3y = 7 and 2x + 4y = 8.

1. Isolate x in the first equation: x = 7 − 3y
2. Substitute the value for x into the second equation: 2(7 − 3y) + 4y = 8
3. Solve for y: 14 − 6y + 4y = 8
14 − 2y = 8
−2y = −6
y = 3
4. Substitute y into either original equation: x = 7 − 3(3)
5. Write the solution as an ordered pair: (
,
)
 

1 answer

Let's go through the solution step by step based on the equations you've provided:

  1. Start with the first equation:
    \[ x + 3y = 7 \]
    Isolate \( x \):
    \[ x = 7 - 3y \]

  2. Substitute \( x = 7 - 3y \) into the second equation:
    \[ 2x + 4y = 8 \]
    \[ 2(7 - 3y) + 4y = 8 \]
    \[ 14 - 6y + 4y = 8 \]

  3. Simplify and solve for \( y \):
    \[ 14 - 2y = 8 \]
    \[ -2y = 8 - 14 \]
    \[ -2y = -6 \]
    \[ y = 3 \]

  4. Substitute \( y = 3 \) back into the equation \( x = 7 - 3y \):
    \[ x = 7 - 3(3) \]
    \[ x = 7 - 9 \]
    \[ x = -2 \]

  5. Finally, write the solution as an ordered pair:
    \[ (-2, 3) \]

So, the solution to the system of equations is \( (-2, 3) \).