What is the solution of the system of equations? -5x+2y=9 3x+5y=7
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Given the systems of equation:
5x+2y=9
3x+5y=7
Determine the solution.
Solution:
The solution can be determined by equating the two equations into one single equation.
5x+2y=9 can be written as,
5x + 2y - 9 = 0
3x+5y=7 can be written as,
3x + 5y - 7 = 0
5x + 2y - 9 = 3x + 5y - 7
Transpose 3x + 5y - 7 on the other side of the equation, note that when transposing a number, the sign changes.
5x + 2y - 9 - 3x - 5y + 7 = 0
Combine like terms.
= 2x - 3y -2
To solve for the solutions, we solve for x and y separately.
x
2x = 3y - 2
x = 3/2y - 1
y
3y = 2x - 2
y = ⅔x - ⅔
Final answer:
x = 3/2y - 1
y = ⅔x - ⅔