Question

What is the solution of the system of equations? -5x+2y=9 3x+5y=7

Answer 1

`\huge\boxed{x=-1,\ y=2\to (-1,\ 2)}`

Explanation:

`\left\{\begin{array}{ccc}-5x+2y=9&\text{multiply both sides by 5}\\3x+5y=7&\text{multiply both sides by (-2)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-25x+10y=45\\-6x-10y=-14\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-31x=31\qquad\text{divide both sides by (-31)}\\.\qquad(-31x)/(-31)=(31)/(-31)\\.\qquad\boxed{x=-1}\\\\\\\text{Put the value of}\ x\ \text{to the second equation:}\\\\3(-1)+5y=7\\-3+5y=7\qquad\text{add 3 to both sides}`

`-3+3+5y=7+3\\5y=10\qquad\text{divide both sides by 5}\\(5y)/(5)=(10)/(5)\\\boxed{y=2}`

Answer 2

The value of x is -1 and value of y is 2

Explanation:

This is a simultaneous equation and we can use the elimination method to solve it

-5x+2y=9 ......................eqn 1

3x+5y=7 .......................eqn 2

Multiply equation 1 by 3 and eqn 2 by 5, the we will have

(-5x+2y=9) × 3

(3x+5y=7) × 5

-15x+6y=27 ..................eqn 3

15x+25y=35 ................eqn 4

Add eqn 3 and 4 together and we will have

31y = 62

Divide both sides by 31 and we will have

y = 2

substitute 2 for y in any equation, but let us pick equation 1

-5x + 2(2) = 9

-5x + 4 = 9

-5x = 9 - 4

-5x = 5

Therefore x = -1