If arcsin (3x - 4y) = 1.571 and arccos (x - y) = 1.047, what is the value of x?
Problem
If $\arcsin (3x - 4y) = 1.571$ and $\arccos (x - y) = 1.047$, what is the value of $x$?
| A. 0.5 | C. 1.5 |
| B. 1.0 | D. 2.0 |
Two Equations, Two Unknowns
Weight of Copper and Tin to Produce an Alloy of 30% Copper and 10% of Tin
Problem
A given alloy contains 20% copper and 5% tin. How many pounds of copper and of tin must be melted with 100 lb of the given alloy to produce another alloy analyzing 30% copper and 10% tin? All percentages are by weight.
B. 17.5 lb copper and 7.5 lb tin
C. 19.5 lb copper and 5.5 lb tin
D. 18.5 lb copper and 6.5 lb tin
Example 07 - Simultaneous Non-Linear Equations of Two Unknowns
Problem
Solve for $x$ and $y$ from the given system of equations.
$\dfrac{3}{x^2} - \dfrac{4}{y^2} = 2$ ← Equation (1)
$\dfrac{5}{x^2} - \dfrac{3}{y^2} = \dfrac{17}{4}$ ← Equation (2)
Example 06 - Simultaneous Non-Linear Equations of Two Unknowns
Problem
Solve for $x$ and $y$ from the given system of equations.
$x^2y + y = 17$ ← Equation (1)
$x^4y^2 + y^2 = 257$ ← Equation (2)
Example 05 - Simultaneous Non-Linear Equations of Two Unknowns
Problem
Solve for x and y from the given system of equations.
$x + 2y = 6$ ← Equation (1)
$\sqrt{x} + \sqrt{y} = 3$ ← Equation (2)
System of Equations
System of Linear Equations
The number of equations should be at least the number of unknowns in order to solve the variables. System of linear equations can be solved by several methods, the most common are the following,
1. Method of substitution
2. Elimination method
3. Cramer's rule
Many of the scientific calculators allowed in board examinations and class room exams are capable of solving system of linear equations of up to three unknowns.
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