Question
Explain which method you used for solving the system of equations in which x represents the number of bottles of water sold and y represents the number of sandwiches sold.
x + y = 390 and 2x + 4y = 1260 make the writing short
x + y = 390 and 2x + 4y = 1260 make the writing short
Answers
GPT-4o mini
To solve the system of equations:
1. \(x + y = 390\) (Equation 1)
2. \(2x + 4y = 1260\) (Equation 2)
I used the substitution method. First, I solved Equation 1 for \(y\):
\[ y = 390 - x \]
Next, I substituted this expression for \(y\) into Equation 2:
\[ 2x + 4(390 - x) = 1260 \]
Simplifying this gives:
\[ 2x + 1560 - 4x = 1260 \]
\[ -2x + 1560 = 1260 \]
\[ -2x = 1260 - 1560 \]
\[ -2x = -300 \]
\[ x = 150 \]
With \(x = 150\), I substituted back to find \(y\):
\[ y = 390 - 150 = 240 \]
Thus, the solution is \(x = 150\) (bottles of water) and \(y = 240\) (sandwiches).
1. \(x + y = 390\) (Equation 1)
2. \(2x + 4y = 1260\) (Equation 2)
I used the substitution method. First, I solved Equation 1 for \(y\):
\[ y = 390 - x \]
Next, I substituted this expression for \(y\) into Equation 2:
\[ 2x + 4(390 - x) = 1260 \]
Simplifying this gives:
\[ 2x + 1560 - 4x = 1260 \]
\[ -2x + 1560 = 1260 \]
\[ -2x = 1260 - 1560 \]
\[ -2x = -300 \]
\[ x = 150 \]
With \(x = 150\), I substituted back to find \(y\):
\[ y = 390 - 150 = 240 \]
Thus, the solution is \(x = 150\) (bottles of water) and \(y = 240\) (sandwiches).