Answer :
Sure, let's solve the given system of equations step-by-step using substitution.
The system of equations is:
[tex]\[ \begin{array}{l} 4x + 3y = 23 \\ x = 5y \end{array} \][/tex]
1. Start with the second equation [tex]\( x = 5y \)[/tex]:
This equation explicitly defines [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]. Now, we can substitute [tex]\( x = 5y \)[/tex] into the first equation.
2. Substitute [tex]\( x = 5y \)[/tex] into the first equation [tex]\( 4x + 3y = 23 \)[/tex]:
[tex]\[ 4(5y) + 3y = 23 \][/tex]
3. Simplify the equation:
[tex]\[ 20y + 3y = 23 \][/tex]
4. Combine like terms:
[tex]\[ 23y = 23 \][/tex]
5. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{23}{23} \][/tex]
[tex]\[ y = 1 \][/tex]
We have found that [tex]\( y = 1 \)[/tex].
6. Substitute [tex]\( y = 1 \)[/tex] back into the equation [tex]\( x = 5y \)[/tex] to find [tex]\( x \)[/tex]:
[tex]\[ x = 5(1) \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the system of equations is:
[tex]\[ x = 5, \quad y = 1 \][/tex]
Therefore, the solution is [tex]\( (5, 1) \)[/tex].
The system of equations is:
[tex]\[ \begin{array}{l} 4x + 3y = 23 \\ x = 5y \end{array} \][/tex]
1. Start with the second equation [tex]\( x = 5y \)[/tex]:
This equation explicitly defines [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]. Now, we can substitute [tex]\( x = 5y \)[/tex] into the first equation.
2. Substitute [tex]\( x = 5y \)[/tex] into the first equation [tex]\( 4x + 3y = 23 \)[/tex]:
[tex]\[ 4(5y) + 3y = 23 \][/tex]
3. Simplify the equation:
[tex]\[ 20y + 3y = 23 \][/tex]
4. Combine like terms:
[tex]\[ 23y = 23 \][/tex]
5. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{23}{23} \][/tex]
[tex]\[ y = 1 \][/tex]
We have found that [tex]\( y = 1 \)[/tex].
6. Substitute [tex]\( y = 1 \)[/tex] back into the equation [tex]\( x = 5y \)[/tex] to find [tex]\( x \)[/tex]:
[tex]\[ x = 5(1) \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the system of equations is:
[tex]\[ x = 5, \quad y = 1 \][/tex]
Therefore, the solution is [tex]\( (5, 1) \)[/tex].
