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3 years ago

Solve the System of Equations -4x + 9y = 14 12x - 10y = - 8

Mathematics

2 answers:

12345 [234]3 years ago

6 0

Answer:

(1, 2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtract Property of Equality

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-4x + 9y = 14

12x - 10y = -8

Step 2: Rewrite Systems

-4x + 9y = 14

Multiply everything by 3: -12x + 27y = 42

Step 3: Redefine Systems

-12x + 27y = 42

12x - 10y = -8

Step 4: Solve for y

Elimination

Combine 2 equations: 17y = 34
Divide 26 on both sides: y = 2

Step 5: Solve for x

Define equation: 12x - 10y = -8
Substitute in y: 12x - 10(2) = -8
Multiply: 12x - 20 = -8
Isolate x term: 12x = 12
Isolate x: x = 1

WARRIOR [948]3 years ago

5 0

Step-by-step explanation:

HERE,

two equation are,

●-4x+9y=14••••••••••••(equation I)

●12x-10y=-8•••••••••••(equation II)

First multiplying 3 in equation I

we get,

$\bold{3×(-4x+9y=14) }$

= $\bold{ -12x+27y=42 }$ ••(equation III)

Then,

we combine the equationii and equation III.

we get that,

$\bold{12x-10y-12x+27y=-8+42 }$

$\bold{\cancel{12x}-10y\cancel{-12x}+27y=-8+42 }$

$\rightsquigarrow$ $\bold{17y=34 }$

$\rightsquigarrow$ $\bold{ y=\dfrac{34}{17} }$

$\rightsquigarrow$ $\boxed{ y=2 }$

Then,

put the value of y in equation II.

WE get,

$\rightsquigarrow$ $\bold{12x-10×2=-8 }$

$\rightsquigarrow$ $\bold{ 12x-20=-8 }$

$\rightsquigarrow$ $\bold{ 12x=-8+20 }$

$\rightsquigarrow$ $\bold{ 12x=12 }$

$\rightsquigarrow$ $\bold{ x=\dfrac{12}{12} }$

$\rightsquigarrow$ $\boxed{ x=1 }$

So,

solution of the two equation (-4x+9y) and (12x-10y=-8) is (1,2)

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