Use Cramers Method to solve a+c=459 and 53a + 16c = 13930

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Use Cramers method to solve:

a + c = 459

53a + 16c = 13930

Check Format

Equation 1 is in the correct format.

Check Format

Equation 2 is in the correct format.

Set up standards equations

Standard equation 1 = ax + by = c and Standard equation 2 = dx + ey = f.

Find a, b, c in ax + by = c

a + c = 459

a = 1, b = 1, c = 459

Find d, e, f in dx + ey = f

53a + 16c = 13930

d = 53, e = 16, f = 13930

Step 1, calculate Delta (Δ):

Δ = a * e - b * d

Δ = (1 * 16) - (1 * 53)

Δ = 16 - 53

Δ = -37

Step 2, calculate the numerator for a

Numerator(a) = c * e - b * f

Numerator(a) = (459 * 16) - (1 * 13930)

Numerator(a) = 7344 - 13930

Numerator(a) = -6586

Step 3, calculate the numerator for c

Numerator(c) = a * f - c * d

Numerator(c) = (1 * 13930) - (459 * 53)

Numerator(c) = 13930 - 24327

Numerator(c) = -10397

Evaluate and solve:

Test Your Knowledge?

1. What are the 3 methods to solve a system of 2 equations?
2. With the elimination method, what are you trying to eliminate?

Common Core State Standards In This Lesson

CCSS.MATH.CONTENT.8.EE.C.8,CCSS.MATH.CONTENT.8.EE.C.8.B

What is the Answer?

c = 281

How does the Simultaneous Equations Calculator work?

Free Simultaneous Equations Calculator - Solves a system of simultaneous equations with 2 unknowns using the following 3 methods:
1) Substitution Method (Direct Substitution)
2) Elimination Method
3) Cramers Method or Cramers Rule Pick any 3 of the methods to solve the systems of equations 2 equations 2 unknowns
This calculator has 2 inputs.

What 1 formula is used for the Simultaneous Equations Calculator?

Δ = a * e - b * d

What 7 concepts are covered in the Simultaneous Equations Calculator?

cramers rule

an explicit formula for the solution of a system of linear equations with as many equations as unknowns

eliminate

to remove, to get rid of or put an end to

equation

a statement declaring two mathematical expressions are equal

simultaneous equations

two or more algebraic equations that share variables

substitute

to put in the place of another. To replace one value with another

unknown

a number or value we do not know

variable

Alphabetic character representing a number

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