Use Cramers Method to solve 2a + 3k = 51 and 3a + k = 45

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Use Cramers method to solve:

2a + 3k = 51

3a + k = 45

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

2a + 3k = 51

a = 2, b = 3, c = 51

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

3a + k = 45

d = 3, e = 1, f = 45

Step 1, calculate Delta (Δ):

Δ = a * e - b * d

Δ = (2 * 1) - (3 * 3)

Δ = 2 - 9

Δ = -7

Step 2, calculate the numerator for a

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

Numerator(a) = (51 * 1) - (3 * 45)

Numerator(a) = 51 - 135

Numerator(a) = -84

Step 3, calculate the numerator for k

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

Numerator(k) = (2 * 45) - (51 * 3)

Numerator(k) = 90 - 153

Numerator(k) = -63

Evaluate and solve:

a =

Numerator(a)

Δ

a =

-84

-7

a = 12

k =

Numerator(k)

Δ

k =

-63

-7

k = 9

What is the Answer?

k = 9

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?

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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