-5x=y+2 2(2x-1)=3-3y What is the solution (x, y) to the system of equations above?
Mathematics · High School · Mon Jan 18 2021
Answered on
Given the equation:
-5x = y + 2
2(2x - 1) = 3- 3y
Solve the systems of equation.
Solution:
Solve first for y for the first and second equation.
-5x = y + 2
y = -5x - 2
2(2x - 1) = 3 - 3y
4x - 2 = 3 - 3y
3y = 3 + 2 - 4x
y = 5/3 - 4/3x
Equate the two solutions into one equation, then solve for x.
-5x - 2 = 5/3 - 4/3x
-2 - 5/3 = -4/3x + 5x
2 can be written as 6/3 and 6 can be written as 15/3
- 6/3 - 5/3 = -4/3x + 15/3x
-11 / 3 = 11 / 3 x
Multiply both sides by 3/11 which is the reciprocal of 11 / 3 to cancel out 11 / 3 x leaving behind x.
(3/11) -11 / 3 = (3/11)11 / 3 x
x = -1
Equate the value of x to the 1st equation and solve for y.
y = -5(-1) - 2
y = 5 - 2
y = 3
Final answer:
x = -1
y = 3