Answer :
To solve the system of equations using the substitution method, follow these steps carefully:
1. Write down the system of equations:
[tex]\[ \begin{array}{l} 2y + 4x = 18 \quad \text{(Equation 1)} \\ 2y - 3x = 4 \quad \text{(Equation 2)} \end{array} \][/tex]
2. Solve one of the equations for one variable in terms of the other.
- Let's solve Equation 1 for [tex]\( y \)[/tex]:
[tex]\[ 2y + 4x = 18 \][/tex]
Subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[ 2y = 18 - 4x \][/tex]
Divide both sides by 2:
[tex]\[ y = 9 - 2x \quad \text{(Equation 3)} \][/tex]
3. Substitute this expression into the other equation.
- Substitute [tex]\( y = 9 - 2x \)[/tex] into Equation 2:
[tex]\[ 2(9 - 2x) - 3x = 4 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
Distribute and combine like terms:
[tex]\[ 18 - 4x - 3x = 4 \][/tex]
Simplify:
[tex]\[ 18 - 7x = 4 \][/tex]
Subtract 18 from both sides:
[tex]\[ -7x = -14 \][/tex]
Divide both sides by -7:
[tex]\[ x = 2 \][/tex]
5. Substitute [tex]\( x = 2 \)[/tex] back into the expression for [tex]\( y \)[/tex]:
[tex]\[ y = 9 - 2(2) \][/tex]
Simplify:
[tex]\[ y = 9 - 4 \][/tex]
[tex]\[ y = 5 \][/tex]
6. Write the solution as an ordered pair:
The solution is [tex]\( (x, y) = (2, 5) \)[/tex].
7. Check the solution:
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 5 \)[/tex] back into the original equations to ensure they are satisfied.
For Equation 1:
[tex]\[ 2(5) + 4(2) = 10 + 8 = 18 \][/tex]
For Equation 2:
[tex]\[ 2(5) - 3(2) = 10 - 6 = 4 \][/tex]
Both equations are satisfied.
8. Choose the correct ordered pair:
The correct answer is:
A. [tex]\( (2, 5) \)[/tex]
1. Write down the system of equations:
[tex]\[ \begin{array}{l} 2y + 4x = 18 \quad \text{(Equation 1)} \\ 2y - 3x = 4 \quad \text{(Equation 2)} \end{array} \][/tex]
2. Solve one of the equations for one variable in terms of the other.
- Let's solve Equation 1 for [tex]\( y \)[/tex]:
[tex]\[ 2y + 4x = 18 \][/tex]
Subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[ 2y = 18 - 4x \][/tex]
Divide both sides by 2:
[tex]\[ y = 9 - 2x \quad \text{(Equation 3)} \][/tex]
3. Substitute this expression into the other equation.
- Substitute [tex]\( y = 9 - 2x \)[/tex] into Equation 2:
[tex]\[ 2(9 - 2x) - 3x = 4 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
Distribute and combine like terms:
[tex]\[ 18 - 4x - 3x = 4 \][/tex]
Simplify:
[tex]\[ 18 - 7x = 4 \][/tex]
Subtract 18 from both sides:
[tex]\[ -7x = -14 \][/tex]
Divide both sides by -7:
[tex]\[ x = 2 \][/tex]
5. Substitute [tex]\( x = 2 \)[/tex] back into the expression for [tex]\( y \)[/tex]:
[tex]\[ y = 9 - 2(2) \][/tex]
Simplify:
[tex]\[ y = 9 - 4 \][/tex]
[tex]\[ y = 5 \][/tex]
6. Write the solution as an ordered pair:
The solution is [tex]\( (x, y) = (2, 5) \)[/tex].
7. Check the solution:
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 5 \)[/tex] back into the original equations to ensure they are satisfied.
For Equation 1:
[tex]\[ 2(5) + 4(2) = 10 + 8 = 18 \][/tex]
For Equation 2:
[tex]\[ 2(5) - 3(2) = 10 - 6 = 4 \][/tex]
Both equations are satisfied.
8. Choose the correct ordered pair:
The correct answer is:
A. [tex]\( (2, 5) \)[/tex]
