Question

PLEASE HELP ME OUT for both questions AND SHOW WORK PLEASEEE

Answer 1

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