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PLEASE HELP ME OUT for both questions AND SHOW WORK PLEASEEE

PLEASE HELP ME OUT for both questions AND SHOW WORK PLEASEEE-example-1
User Hitttt
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1 Answer

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Answer:

8) x = 5, y = -5

10) x = -2.8, y = 3.4

Explanation:

To solve a system of linear equations we can use either the substitution method or the elimination method.

Question 8

Given system of linear equations:


\begin{cases}-6x-3y=-15\\6y+6x=0\end{cases}

Solve the given system of linear equations using the elimination method.

Add the two equations to eliminate the term in x:


\begin{array}{crcccl}&-6x & - & 3y & = & -15\\+&(6x & + &6y & = & \;\;\;\;0)\\\cline{2-6}&0&+&3y&=&-15\end{array}

Solve the resulting equation for y by dividing both sides by 3:


\implies 3y / 3 &=-15 / 3


\implies y=-5

Substitute the found value of y into the second equation and solve for x:


\implies 6(-5)+6x=0


\implies -30+6x=0


\implies 6x=30


\implies 6x / 6=30 / 6


\implies x=5

Therefore, the solution to the given system of equations is:

  • x = 5
  • y = -5

Question 10


\begin{cases}-x+3y=13\\-3x-y=5\end{cases}

Solve the given system of linear equations using the substitution method.

Rearrange the first equation to isolate x:


\implies -x+3y=13


\implies 3y=x+13


\implies x=3y-13

Substitute the expression for x into the second equation and solve for y:


\implies -3(3y-13)-y=5


\implies -9y+39-y=5


\implies -10y+39=5


\implies -10y=-34


\implies -10y/ -10=-34 / -10


\implies y=3.4

Substitute the found value of y into the expression for x and solve for x:


\implies x=3(3.4)-13


\implies x=10.2-13


\implies x=-2.8

Therefore, the solution to the given system of equations is:

  • x = -2.8
  • y = 3.4
User Crysta
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