Use the substitution method to solve the system of equations. Choose the correct ordered pair.

[tex]
\begin{array}{l}
2y + 4x = 18 \\
2y - 3x = 4
\end{array}
[/tex]

A. [tex]\((2, 5)\)[/tex]

B. [tex]\((6, -3)\)[/tex]

C. [tex]\((5, -1)\)[/tex]

D. [tex]\((3, 3)\)[/tex]



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]