Question

Solve the system of equations.
6x–5y=27

3x+5y=36

Answer 1

Solve the system of two linear equations.
−3x−4y=−23
3x−5y=5

Answer 2

To solve this system of equations, we can add the two equations together to eliminate the variable y:

6x - 5y + 3x + 5y = 27 + 36
9x = 63
x = 63/9
x = 7

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

6(7) - 5y = 27
42 - 5y = 27
-5y = -15
y = 3

Therefore, the solution to the system of equations is x = 7 and y = 3.

Answer 3

To solve this system of equations, we can use the method of elimination.

1. Multiply the first equation by 3 to match the coefficients of x in both equations:
-9x - 12y = -69

2. Rewrite the second equation:
3x - 5y = 5

3. Add the two equations together to eliminate x:
-9x - 12y + 3x - 5y = -69 + 5
-6y = -64
y = -64 / -6
y = 32 / 3

4. Substitute the value of y back into one of the original equations (I will use the first equation):
-3x - 4(32/3) = -23
-3x - 128 / 3 = -23
-3x = -23 * 3 + 128
-3x = -69 + 128
-3x = 59
x = 59 / -3
x = -59 / 3

Therefore, the solution to the system of equations is x = -59/3 and y = 32/3.