Math Snap

STEP 1

1. We are given a system of two linear equations.
2. The goal is to find the values of $x$ and $y$ that satisfy both equations simultaneously.
3. We will use the substitution method to solve the system.

STEP 2

1. Set the equations equal to each other.
2. Solve for $x$.
3. Substitute the value of $x$ back into one of the original equations to find $y$.
4. Verify the solution by checking both equations.

STEP 3

Since both equations are equal to $y$, we can set them equal to each other:
$$-2x + 2 = 7x + 11$$

STEP 4

To solve for $x$, first get all terms involving $x$ on one side of the equation and constant terms on the other:
$$-2x - 7x = 11 - 2$$

STEP 5

Combine like terms:
$$-9x = 9$$

STEP 6

Divide both sides by $-9$ to solve for $x$:
$$x = -1$$

STEP 7

Substitute $x = -1$ back into one of the original equations to find $y$. We'll use the first equation:
$$y = -2(-1) + 2$$

STEP 8

Simplify the equation:
$$y = 2 + 2 = 4$$

STEP 9

Verify the solution by substituting $x = -1$ and $y = 4$ into the second equation:
$$y = 7(-1) + 11$$

Simplify the equation:
$$4 = -7 + 11$$ $$4 = 4$$ Both sides are equal, confirming our solution is correct.
The solution to the system of equations is:
$$x = -1, \quad y = 4$$