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Sagot :
To solve the system of equations by substitution, follow these steps:
Given the system:
[tex]\[ \begin{array}{l} y = -7x - 11 \\ -4x - 5y = 24 \end{array} \][/tex]
1. Substitute the expression for [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[ y = -7x - 11 \][/tex]
Substitute [tex]\( y \)[/tex] in [tex]\(-4x - 5y = 24\)[/tex]:
[tex]\[ -4x - 5(-7x - 11) = 24 \][/tex]
2. Simplify the equation:
[tex]\[ -4x + 35x + 55 = 24 \][/tex]
3. Combine like terms:
[tex]\[ 31x + 55 = 24 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ 31x = 24 - 55 \][/tex]
[tex]\[ 31x = -31 \][/tex]
[tex]\[ x = -1 \][/tex]
5. Substitute [tex]\( x = -1 \)[/tex] back into the first equation to solve for [tex]\( y \)[/tex]:
[tex]\[ y = -7(-1) - 11 \][/tex]
[tex]\[ y = 7 - 11 \][/tex]
[tex]\[ y = -4 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ (x, y) = (-1, -4) \][/tex]
Given the system:
[tex]\[ \begin{array}{l} y = -7x - 11 \\ -4x - 5y = 24 \end{array} \][/tex]
1. Substitute the expression for [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[ y = -7x - 11 \][/tex]
Substitute [tex]\( y \)[/tex] in [tex]\(-4x - 5y = 24\)[/tex]:
[tex]\[ -4x - 5(-7x - 11) = 24 \][/tex]
2. Simplify the equation:
[tex]\[ -4x + 35x + 55 = 24 \][/tex]
3. Combine like terms:
[tex]\[ 31x + 55 = 24 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ 31x = 24 - 55 \][/tex]
[tex]\[ 31x = -31 \][/tex]
[tex]\[ x = -1 \][/tex]
5. Substitute [tex]\( x = -1 \)[/tex] back into the first equation to solve for [tex]\( y \)[/tex]:
[tex]\[ y = -7(-1) - 11 \][/tex]
[tex]\[ y = 7 - 11 \][/tex]
[tex]\[ y = -4 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ (x, y) = (-1, -4) \][/tex]
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