What is the solution to this system of equations? 4x + 5y = 7 3x – 2y = –12
Mathematics · Middle School · Thu Feb 04 2021
Answered on
Given the equations:
4x + 5y = 7
3x - 2y = -12
Determine the solutions of the equation.
Solution:
In order to solve the solutions of the equation, we first solve for y for the first equation then substitute the value of y to the 2nd equation.
4x + 5y = 7
Transpose 4x to the other side of the equation hence it must be taken to note that in transposing a number the sign changes. After transposing, we need to divide 5 on both sides of the equation, in order to cancel out 5y, leaving behind y.
4x + 5y = 7
5y = 7 - 4x
5y/5 = (7 - 4x)/5
y = 35 - 4/5x
Substitute the value of y of the first equation to the second equation.
3x - (7)(35 - 4/5x) = 7
3x - 245 - 28/5x = 7
3x can be written 15/5x.
15/5x - 245 - 28/5x = 7
-13/5x = 7 + 245
-13/5x = 252
Divide both sides by -5/13x in order to cancel out -13/5x, leaving behind x.
(-5/13)(-13/5x) = (252)(-5/13)
x = -10.24
Final answer:
x = -10.24