Question

solving systems of equations by
solve each system by substitution.

1. $y=6x-11$

$-2x-3y=-7$

Explanation:

Step1: Substitute $y$ into second equation

Substitute $y=6x-11$ into $-2x-3y=-7$:
$$-2x - 3(6x - 11) = -7$$

Step2: Expand and simplify equation

Distribute and combine like terms:
$$-2x - 18x + 33 = -7$$
$$-20x + 33 = -7$$

Step3: Solve for $x$

Isolate $x$ by moving constants:
$$-20x = -7 - 33$$
$$-20x = -40$$
$$x = \frac{-40}{-20} = 2$$

Step4: Solve for $y$

Substitute $x=2$ into $y=6x-11$:
$$y = 6(2) - 11 = 12 - 11 = 1$$

Answer:

$x=2$, $y=1$