Question

Solve the system by elimination method 7x+5y=-25 5x+3y=-23

Answer 1

The solution is x = -10, y = 9

Step-by-step explanation:

Given equations are:

$7x+5y = -25\ \ \ \ Eqn\ 1\\5x+3y = -23\ \ \ Eqn\ 2$

Multiplying equation 1 by 3

$3(7x+5y) = -25 * 3\\21x+15y = -75\ \ \ Eqn\ 3$

Multiplying equation 2 by 5

$5(5x+3y) = -23 * 5\\25x+15y = -115\ \ \ Eqn\ 2$

Subtracting equation 3 from equation 4

$(25x+15y) - (21x+15y) = -115 - (-75)\\25x+15y-21x-15y = -115+75\\4x = -40$

Dividing both sides by 4

$\frac{4x}{4} = \frac{-40}{4}\\x = -10$

Putting x = -1 in equation 1

$7(-10)+5y = -25\\-70+5y = -25\\5y = -25+70\\5y = 45$

Dividing both sides by 5

$\frac{5y}{5} = \frac{45}{5}\\y = 9$

Hence,

The solution is x = -10, y = 9

Keywords: Linear equations, variables

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