Is (5,2) a solution of 4x-2y=-6
I said no, am I right?
I am working on another problem where they want to know if this system of equations is perpendicular or parallel or neither,5x+4y=2, 4x-5y=4 I said neither. Is this right?
I am to solve by using elimination: 2x+3y=1, 4x+6y=2
I keep getting o, no solution. What am I doing wrong?
#1 is cirrect
#2 is incorrect. The lines are perpendicular because the product of the slopes (-5/4 and 4/5) is -1.
#3 You are doing nothing wrong. The two equations are really the same line. There is no UNIQUE solution; there are an infinite number. x = 1/2, y = 0 would be one of them. y = 1/3, x = 0 would be another.
To determine if a given point is a solution to an equation, you need to substitute the values of the coordinates into the equation and check if the equation is satisfied.
1. Is (5,2) a solution of 4x-2y=-6?
To verify, plug in the values of x and y into the equation:
4(5) - 2(2) = -6
20 - 4 = -6
16 = -6
Since 16 is not equal to -6, the equation is not satisfied. Therefore, (5,2) is not a solution to the given equation. You were correct.
2. Are the equations 5x+4y=2 and 4x-5y=4 perpendicular, parallel, or neither?
To determine this, we'll compare the slopes of the two equations. The slope-intercept form of a line is y = mx + b, where m is the slope.
In the given equations, we can rewrite them in slope-intercept form:
5x + 4y = 2 => 4y = -5x + 2 => y = (-5/4)x + 1/2
4x - 5y = 4 => -5y = -4x + 4 => y = (4/5)x - 4/5
Now, compare the slopes:
The slope of the first equation, y = (-5/4)x + 1/2, is -5/4.
The slope of the second equation, y = (4/5)x - 4/5, is 4/5.
Since the slopes are different (not equal to each other or their negative reciprocals), the two lines are neither parallel nor perpendicular. Your answer of "neither" is correct.
3. Solving using elimination: 2x+3y=1 and 4x+6y=2.
To solve this system of equations using elimination, we can multiply the first equation by -2 and the second equation by 2 to make the coefficients of x in both equations equal:
-2(2x + 3y) = -2(1) => -4x - 6y = -2
2(4x + 6y) = 2(2) => 8x + 12y = 4
Now, add the two equations together:
(-4x - 6y) + (8x + 12y) = (-2) + (4)
4x + 6y = 2
Notice that the resulting equation is equivalent to the given second equation of the system. This means that the two equations represent the same line, and the system has infinitely many solutions. Therefore, your answer of "no solution" is incorrect. The correct answer is "infinitely many solutions."