Answer :
Answer:
To find the values of \( x \) and \( y \) for the system of equations:
1. \( 2x + 3y = 21 \)
2. \( 6x + 7y = 53 \)
We can use either the substitution method or the elimination method. Here, I'll use the elimination method.
First, let's eliminate one of the variables. We can start by eliminating \( x \).
1. Multiply the first equation by 3 to align the coefficients of \( x \):
\[ 3(2x + 3y) = 3(21) \]
\[ 6x + 9y = 63 \]
2. Now we have the system:
\[ 6x + 9y = 63 \]
\[ 6x + 7y = 53 \]
3. Subtract the second equation from the first:
\[ (6x + 9y) - (6x + 7y) = 63 - 53 \]
\[ 6x + 9y - 6x - 7y = 10 \]
\[ 2y = 10 \]
\[ y = 5 \]
Now that we have \( y \), we can substitute it back into one of the original equations to find \( x \). Using the first equation:
\[ 2x + 3y = 21 \]
\[ 2x + 3(5) = 21 \]
\[ 2x + 15 = 21 \]
\[ 2x = 6 \]
\[ x = 3 \]
Thus, the solution to the system of equations is \( x = 3 \) and \( y = 5 \).
Answer:
Step-by-step explanation: 2x+3y=21
2x = 21-3y
multiply both sides with 3
6x = 63 - 9y
also given 6x+7y=53
63-9y+7y=53
63-53=9y-7y
10=2y
y=5
2x = 21-3y
2x = 21-15
2x = 6
x=6