Answer :
To solve the given system of equations:
[tex]\[ \left\{ \begin{array}{l} y = 6x - 11 \\ -2x - 3y = -7 \end{array} \right. \][/tex]
we will follow a systematic approach.
1. Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
The first equation is:
[tex]\[ y = 6x - 11 \][/tex]
Substitute [tex]\( y = 6x - 11 \)[/tex] into the second equation:
[tex]\[ -2x - 3(6x - 11) = -7 \][/tex]
2. Simplify and solve for [tex]\( x \)[/tex]:
Distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[ -2x - 18x + 33 = -7 \][/tex]
Combine like terms:
[tex]\[ -20x + 33 = -7 \][/tex]
Subtract 33 from both sides:
[tex]\[ -20x = -7 - 33 \][/tex]
[tex]\[ -20x = -40 \][/tex]
Divide both sides by [tex]\(-20\)[/tex]:
[tex]\[ x = \frac{-40}{-20} \][/tex]
[tex]\[ x = 2 \][/tex]
3. Substitute [tex]\( x = 2 \)[/tex] back into the first equation to find [tex]\( y \)[/tex]:
Using the first equation:
[tex]\[ y = 6x - 11 \][/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 6(2) - 11 \][/tex]
[tex]\[ y = 12 - 11 \][/tex]
[tex]\[ y = 1 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ (x, y) = (2, 1) \][/tex]
Among the given options, the correct solution is:
[tex]\[ (2, 1) \][/tex]
[tex]\[ \left\{ \begin{array}{l} y = 6x - 11 \\ -2x - 3y = -7 \end{array} \right. \][/tex]
we will follow a systematic approach.
1. Substitute [tex]\( y \)[/tex] from the first equation into the second equation:
The first equation is:
[tex]\[ y = 6x - 11 \][/tex]
Substitute [tex]\( y = 6x - 11 \)[/tex] into the second equation:
[tex]\[ -2x - 3(6x - 11) = -7 \][/tex]
2. Simplify and solve for [tex]\( x \)[/tex]:
Distribute the [tex]\(-3\)[/tex] inside the parentheses:
[tex]\[ -2x - 18x + 33 = -7 \][/tex]
Combine like terms:
[tex]\[ -20x + 33 = -7 \][/tex]
Subtract 33 from both sides:
[tex]\[ -20x = -7 - 33 \][/tex]
[tex]\[ -20x = -40 \][/tex]
Divide both sides by [tex]\(-20\)[/tex]:
[tex]\[ x = \frac{-40}{-20} \][/tex]
[tex]\[ x = 2 \][/tex]
3. Substitute [tex]\( x = 2 \)[/tex] back into the first equation to find [tex]\( y \)[/tex]:
Using the first equation:
[tex]\[ y = 6x - 11 \][/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 6(2) - 11 \][/tex]
[tex]\[ y = 12 - 11 \][/tex]
[tex]\[ y = 1 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ (x, y) = (2, 1) \][/tex]
Among the given options, the correct solution is:
[tex]\[ (2, 1) \][/tex]
-2x -3y = -7
-3y = 2x -7
y = -2/3x +7/3 (lets call this equation 1)
y = 6x -11 (lets call this equation 2)
Now, substitute equation 1 into equation 2.
-2/3x + 7/3 = 6x -11
-20/3x = -40/3
x = 2
Now, substitute x=2 back into equation 2.
y = 6(2) -11
y = 1
Hence the answer is D (2,1).
-3y = 2x -7
y = -2/3x +7/3 (lets call this equation 1)
y = 6x -11 (lets call this equation 2)
Now, substitute equation 1 into equation 2.
-2/3x + 7/3 = 6x -11
-20/3x = -40/3
x = 2
Now, substitute x=2 back into equation 2.
y = 6(2) -11
y = 1
Hence the answer is D (2,1).
