Solve by Substitution 4x-5y=-17 , 3x+2y=-7

Problem

{[4*x−5*y=−17],[3*x+2*y=−7])

Solution

1. Solve the second equation for y to express it in terms of x

3*x+2*y=−7

2*y=−3*x−7

y=−1.5*x−3.5

2. Substitute the expression for y into the first equation.

4*x−5*(−1.5*x−3.5)=−17

3. Distribute the constant and combine like terms to solve for x

4*x+7.5*x+17.5=−17

11.5*x+17.5=−17

11.5*x=−34.5

x=−3

4. Substitute the value of x back into the expression for y

y=−1.5*(−3)−3.5

y=4.5−3.5

y=1

Final Answer

(x,y)=(−3,1)

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