Certainly! Let's solve the system of equations step-by-step:
We have two equations:
1. \( x = 5 - 2y \)
2. \( 6y = 10 - 3x \)
Step 1: Substitute the expression for \( x \) from the first equation into the second equation.
From equation (1):
[tex]\[ x = 5 - 2y \][/tex]
Substitute \( x = 5 - 2y \) into equation (2):
[tex]\[ 6y = 10 - 3(5 - 2y) \][/tex]
Step 2: Simplify the equation obtained after substitution.
[tex]\[ 6y = 10 - 3(5 - 2y) \][/tex]
[tex]\[ 6y = 10 - 15 + 6y \][/tex]
[tex]\[ 6y = 6y - 5 \][/tex]
Step 3: Isolate the variable terms on one side of the equation.
Subtract \( 6y \) from both sides:
[tex]\[ 6y - 6y = -5 \][/tex]
[tex]\[ 0 = -5 \][/tex]
Step 4: Analyze the resultant equation.
The equation \( 0 = -5 \) is a contradiction. This suggests that there is no solution that satisfies both equations simultaneously.
Therefore, the system of equations has no solution. In other words, there are no values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations at the same time.
