-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