Question

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

Answer 1

To solve the system of equations, we can use the method of elimination.
First, we can multiply the second equation by 2 to make the coefficients of x in both equations opposite:
2(3x - 5y) = 2(5)
Simplifying this equation, we get:
6x - 10y = 10

Now we can add this equation to the first equation:
(-3x - 4y) + (6x - 10y) = -23 + 10
Combining like terms, we get:
3x - 14y = -13

Now we have a new equation:
3x - 14y = -13

We can solve for x in this equation:
3x = 14y - 13
x = (14y - 13)/3

We can substitute this value of x back into the original second equation:
3(14y - 13)/3 - 5y = 5
14y - 13 - 5y = 5
9y = 18
y = 2

Substituting the value of y back into the equation x = (14y - 13)/3, we get:
x = (14(2) - 13)/3
x = (28 - 13)/3
x = 5

Therefore, the solution to the system of equations is x = 5 and y = 2.