Answer :
To solve the system of linear equations:
[tex]\[ \begin{cases} 3x + 7y = 1 \\ y = x - 7 \end{cases} \][/tex]
we'll use the substitution method given that the second equation is already solved for [tex]\( y \)[/tex]:
1. Substitute [tex]\( y = x - 7 \)[/tex] into the first equation [tex]\( 3x + 7y = 1 \)[/tex]:
[tex]\[ 3x + 7(x - 7) = 1 \][/tex]
2. Simplify the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 3x + 7x - 49 = 1 \][/tex]
Combine like terms:
[tex]\[ 10x - 49 = 1 \][/tex]
Add 49 to both sides:
[tex]\[ 10x = 50 \][/tex]
Divide both sides by 10:
[tex]\[ x = 5 \][/tex]
3. Substitute [tex]\( x = 5 \)[/tex] back into the second equation [tex]\( y = x - 7 \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[ y = 5 - 7 \][/tex]
[tex]\[ y = -2 \][/tex]
So, the solution to the system of equations is [tex]\( (5, -2) \)[/tex].
4. Verify which option matches this solution:
[tex]\[ \begin{array}{l} A: (2, -5) \\ B: (5, -2) \\ C: (4, -3) \\ D: (3, -4) \end{array} \][/tex]
The correct answer is [tex]\( (5, -2) \)[/tex], which corresponds to.
[tex]\[ \boxed{B} \][/tex]
[tex]\[ \begin{cases} 3x + 7y = 1 \\ y = x - 7 \end{cases} \][/tex]
we'll use the substitution method given that the second equation is already solved for [tex]\( y \)[/tex]:
1. Substitute [tex]\( y = x - 7 \)[/tex] into the first equation [tex]\( 3x + 7y = 1 \)[/tex]:
[tex]\[ 3x + 7(x - 7) = 1 \][/tex]
2. Simplify the equation to solve for [tex]\( x \)[/tex]:
[tex]\[ 3x + 7x - 49 = 1 \][/tex]
Combine like terms:
[tex]\[ 10x - 49 = 1 \][/tex]
Add 49 to both sides:
[tex]\[ 10x = 50 \][/tex]
Divide both sides by 10:
[tex]\[ x = 5 \][/tex]
3. Substitute [tex]\( x = 5 \)[/tex] back into the second equation [tex]\( y = x - 7 \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[ y = 5 - 7 \][/tex]
[tex]\[ y = -2 \][/tex]
So, the solution to the system of equations is [tex]\( (5, -2) \)[/tex].
4. Verify which option matches this solution:
[tex]\[ \begin{array}{l} A: (2, -5) \\ B: (5, -2) \\ C: (4, -3) \\ D: (3, -4) \end{array} \][/tex]
The correct answer is [tex]\( (5, -2) \)[/tex], which corresponds to.
[tex]\[ \boxed{B} \][/tex]
