2x - 3y = 2
The graph of this equation is a straight line, which crosses the y-axis where [ y = -2/3 ]
and has a slope of 2/3 .
x + 2y = 8
The graph of this one is also a straight line, which crosses the y-axis where [ y = 4 ]
and has a slope of -1/2 .
The equation ( x + y = 6 ) represents a line with a slope of -1 that intersects the y-axis at (0, 6) and the x-axis at (6, 0). The equation ( x - y = 6 ) represents a line with a slope of 1 that intersects the y-axis at (-6, 0) and the x-axis at (6, 0). These two lines intersect at the point (6, 0) and are perpendicular to each other.
All the lines meet at one point: a single solution. All the lines are the same: infinitely many solutions. At least one of the lines does not pass through the point of intersection of the others: no solution.
Equations that have letters are just called equations, but there are types 1, 2, 3, 4 and ratio type equations. Ratio type equations are the ones where it is a fraction on both sides of the equals sign. Equation (Type 2): x+1-5=12 Ratio Type Equation: 21/7=42-x/3
A system of two linear equations in two unknowns can have three possible types of solutions: exactly one solution (when the lines intersect at a single point), no solutions (when the lines are parallel and never intersect), or infinitely many solutions (when the two equations represent the same line). Thus, there are three potential outcomes for such a system.
The three types of linear equations are: Consistent Dependent, Consistent Independent, and Inconsistent.
Invisible lines!
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If you refer to linear equations, graphed as straight lines, two inconsistent equations would result in two parallel lines.
Generally, both types of equation contain an equals sign and some combination of numbers and/or variables. That is the only thing I can think of that is common between all types of nonlinear and linear equations.
There is only one line in the x-y plane and that is a straight line with a gradient of -1, passing through the point (0, 10)
x+y=12 is a linear (straight line) equation in the xy-plane. Alternate forms are y=12-x and x=12-y. The form y=12-x is most familiar, and it is a straight line with a slope of -1 that intercepts the y-axis at 12 and the x-axis at 12.
All the lines meet at one point: a single solution. All the lines are the same: infinitely many solutions. At least one of the lines does not pass through the point of intersection of the others: no solution.
Equations that have letters are just called equations, but there are types 1, 2, 3, 4 and ratio type equations. Ratio type equations are the ones where it is a fraction on both sides of the equals sign. Equation (Type 2): x+1-5=12 Ratio Type Equation: 21/7=42-x/3
Algebraic equations, trigenometric equations, linear equations, geometric equations, partial differential equations, differential equations, integrals to name a few.
In two dimensions, parallel ones. In three dimensions, either parallel or skew ones.
Keywords match types are classified below:-Broad MatchBroad Match ModifierPhrase MatchExact MatchNegative Match
There are different types of lines: curved lines, dotted lines, wavy lines and straight lines.