Answer :
To solve the system of linear equations:
[tex]\[ \begin{array}{l} 2x + 7y = 4 \\ -4x - 3y = 14 \end{array} \][/tex]
we follow these steps:
1. Multiply the first equation by 2 to make the coefficients of [tex]\( x \)[/tex] in the two equations opposites of each other:
[tex]\[ 2(2x + 7y) = 2(4) \][/tex]
This yields:
[tex]\[ 4x + 14y = 8 \][/tex]
2. Now, we have the modified system of equations:
[tex]\[ \begin{array}{l} 4x + 14y = 8 \\ -4x - 3y = 14 \end{array} \][/tex]
3. Add the two equations to eliminate [tex]\( x \)[/tex]:
[tex]\[ (4x + 14y) + (-4x - 3y) = 8 + 14 \][/tex]
Simplifying the left side and summing the right side, we obtain:
[tex]\[ 4x - 4x + 14y - 3y = 22 \\ 11y = 22 \][/tex]
4. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{22}{11} \\ y = 2 \][/tex]
5. Substitute the value of [tex]\( y \)[/tex] back into the first equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 2x + 7(2) = 4 \\ 2x + 14 = 4 \\ 2x = 4 - 14 \\ 2x = -10 \\ x = \frac{-10}{2} \\ x = -5 \][/tex]
Therefore, the solution to the system of equations is the ordered pair:
[tex]\[ (-5,2) \][/tex]
[tex]\[ \begin{array}{l} 2x + 7y = 4 \\ -4x - 3y = 14 \end{array} \][/tex]
we follow these steps:
1. Multiply the first equation by 2 to make the coefficients of [tex]\( x \)[/tex] in the two equations opposites of each other:
[tex]\[ 2(2x + 7y) = 2(4) \][/tex]
This yields:
[tex]\[ 4x + 14y = 8 \][/tex]
2. Now, we have the modified system of equations:
[tex]\[ \begin{array}{l} 4x + 14y = 8 \\ -4x - 3y = 14 \end{array} \][/tex]
3. Add the two equations to eliminate [tex]\( x \)[/tex]:
[tex]\[ (4x + 14y) + (-4x - 3y) = 8 + 14 \][/tex]
Simplifying the left side and summing the right side, we obtain:
[tex]\[ 4x - 4x + 14y - 3y = 22 \\ 11y = 22 \][/tex]
4. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{22}{11} \\ y = 2 \][/tex]
5. Substitute the value of [tex]\( y \)[/tex] back into the first equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 2x + 7(2) = 4 \\ 2x + 14 = 4 \\ 2x = 4 - 14 \\ 2x = -10 \\ x = \frac{-10}{2} \\ x = -5 \][/tex]
Therefore, the solution to the system of equations is the ordered pair:
[tex]\[ (-5,2) \][/tex]
