Solve the system by substitution.
--5x - 9y = 33
-Y - 1 = x

(12/7, -19/7)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define systems

--5x - 9y = 33

-y - 1 = x

Step 2: Simplify systems

5x - 9y = 33

-y - 1 = x

Step 3: Solve for y

Substitute:                              5(-y - 1) - 9y = 33Distribute 5:                            -5y - 5 - 9y = 33Combine like terms:               -14y - 5 = 33Isolate y term:                         -14y = 38Isolate y:                                  y = -19/7

Step 4: Solve for x

Define:                              -y - 1 = xSubstitute:                        -(-19/7) - 1 = xSimplify:                            19/7 - 1 = xSubtract:                           12/7 = xRewrite:                             x = 12/7

And we have our final answer!

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12