find the solution of the system of equations.\n$5x + 10y = -5$\n$-5x - y = 32$
find the solution of the system of equations.\n$5x + 10y = -5$\n$-5x - y = 32$
Answer
Explanation:
Step1: Add the two equations to eliminate (x)
The system of equations is: [ \begin{cases} 5x + 10y = -5 \ -5x - y = 32 \end{cases} ] Adding the left - hand sides and the right - hand sides of the two equations: ((5x + 10y)+(-5x - y)=-5 + 32) Simplify the left - hand side: (5x-5x + 10y-y=9y) Simplify the right - hand side: (27) So we get the equation (9y=27)
Step2: Solve for (y)
From (9y = 27), divide both sides by (9): (y=\frac{27}{9}=3)
Step3: Substitute (y = 3) into one of the original equations to solve for (x)
We substitute (y = 3) into the first equation (5x+10y=-5) (5x+10\times3=-5) (5x + 30=-5) Subtract (30) from both sides: (5x=-5 - 30=-35) Divide both sides by (5): (x=\frac{-35}{5}=-7)
Answer:
The solution of the system of equations is (x=-7), (y = 3)