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, 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?
5x+4y=2, 4x-5y=4....I said neither on whether the line was parallel or perpendicular or neither.
To check if (5,2) is a solution of the equation 4x-2y=-6, substitute the values of x and y into the equation:
4(5) - 2(2) = -6
20 - 4 = -6
16 ≠ -6
Since the equation is not satisfied when (x,y) = (5,2), your initial answer of no is correct.
To determine if the system of equations is perpendicular, parallel, or neither, we need to compare the slopes of the two equations.
The given equations are:
2x + 3y = 1 (equation 1)
4x + 6y = 2 (equation 2)
Both equations can be rewritten in slope-intercept form (y = mx + b) to determine their slopes.
For equation 1:
2x + 3y = 1
3y = -2x + 1
y = (-2/3)x + 1/3
For equation 2:
4x + 6y = 2
6y = -4x + 2
y = (-4/6)x + 1/3
y = (-2/3)x + 1/3
The slopes of both equations are -2/3, which means they have the same slope. Therefore, the system of equations is parallel.
Now, let's solve the system of equations using elimination:
2x + 3y = 1 (equation 1)
4x + 6y = 2 (equation 2)
To eliminate one variable, we need to multiply equation 1 by -2 and equation 2 by 1/2:
-4x - 6y = -2 (multiplied equation 1 by -2)
2x + 3y = 1 (equation 1)
4x + 6y = 2 (equation 2)
Now, add the equations:
(2x - 4x) + (3y + 6y) = 1 + (-2)
-2x + 9y = -1
The equations -2x + 9y = -1 and 4x + 6y = 2 form a contradictory system. This means there is no solution to the system of equations.
So, your answer of no solution is correct.
To determine if (5,2) is a solution for the equation 4x-2y=-6, you need to substitute the values of x and y into the equation and check if it holds true. Let's perform the substitution:
4(5) - 2(2) = -6
20 - 4 = -6
16 = -6
Since 16 is not equal to -6, (5,2) is not a solution to the equation. Therefore, your initial answer of "no" is correct.
For the second problem where you need to determine if the system of equations is perpendicular, parallel, or neither, you need to examine the slopes of the two equations. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals of each other, the lines are perpendicular. If neither of these conditions is met, the lines are neither parallel nor perpendicular.
Let's find the slopes of the given system of equations:
1) 2x + 3y = 1
To find the slope, we need to rewrite the equation in slope-intercept form (y = mx + b):
3y = -2x + 1
y = (-2/3)x + 1/3
The slope of the first equation is -2/3.
2) 4x + 6y = 2
Again, we rewrite the equation in slope-intercept form:
6y = -4x + 2
y = (-4/6)x + 2/6
y = (-2/3)x + 1/3
The slope of the second equation is also -2/3.
Since the slopes of the two equations are equal (-2/3), the lines are parallel. Therefore, your answer of "neither" in this case is incorrect.
Lastly, to solve the system of equations 2x + 3y = 1 and 4x + 6y = 2 using the elimination method, we need to eliminate one of the variables by multiplying one of the equations. Let's multiply the first equation by 2 to make both coefficients of x in both equations equal:
2(2x + 3y) = 2(1)
4x + 6y = 2
Now we can see that both equations are identical. They represent the same line. This means there are infinitely many solutions that satisfy both equations, making the system dependent. Therefore, your answer of no solution is incorrect.
To summarize, you got the first question right, the second question wrong, and the third question wrong. It's essential to double-check your work and calculations to make sure you arrive at the correct answers.