2x - 3y = 16
5x - 3y = 13
Solve the system of equations.
Responses
A (1, -143
)(1, - 14 3 )
B (5, 4)(5, 4)
C (5, -2)(5, -2)
D (-1, -6)(-1, -6)
E (-6, -1)
Subtracting the first equation from the second, we get:
3x = -3
x = -1
Substituting this into the first equation:
2(-1) - 3y = 16
-2 - 3y = 16
-3y = 18
y = -6
Therefore, the solution is (−1, −6), which corresponds to option D.
To solve the system of equations:
Step 1: Rearrange the equations in a standard form, where the variables are on the left side and the constants are on the right side:
2x - 3y = 16 --> 2x - 16 = 3y
5x - 3y = 13 --> 5x - 13 = 3y
Step 2: Equate the two expressions for y:
2x - 16 = 5x - 13
Step 3: Simplify and solve for x:
2x - 5x = -13 + 16
-3x = 3
x = -1
Step 4: Substitute the value of x into one of the original equations (let's use the first equation) and solve for y:
2(-1) - 3y = 16
-2 - 3y = 16
-3y = 16 + 2
-3y = 18
y = -6
The solution to the system of equations is therefore x = -1 and y = -6.
So, the correct answer is D: (-1, -6).