Question

Solve the systems of equations.

Answer 1

Answer: x=2, y=-8

Step-by-step explanation: there are a couple of different methods you can use, my favourite is substitution

to do this, find a value of x or y from one equation and plug it into the other. let's use x in this case

so we have 13x-6y=22 and x=y+6

for the x value of the first equation, plug in x=y+6 from the second equation to get:

13(y+6)-6y=22

then you solve for y,

13y+78-6y=22

7y=-56

y=-8

then to solve for x, plug in your y value to either of the first 2 equations. lets use x=y+6

so you'd have x=(-8)+6 to give you x=2

hope this helps!

Answer 2

The solution to the system of equations is x=4.

The value of y in the system of equations is y=−2.

To solve the given system of equations, we can employ the substitution method. The two equations are:

`13x - 6y &= 22 \\x &= y + 6\end{align*} \]First, we substitute the expression \( y + 6 \) for \( x \) in the first equation:\[ 13(y + 6) - 6y = 22 \]Simplifying this equation leads to \( y = -2 \). Once we have \( y \), we substitute this value back into the second equation to find \( x \):\[ x = -2 + 6 \]This yields \( x = 4 \). Therefore, the solution to the system of equations is \( x = 4 \) and \( y = -2 \).`