Discover new perspectives and gain insights with IDNLearn.com. Our platform offers reliable and detailed answers, ensuring you have the information you need.

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]


Sagot :

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]