Lines X and Y are parallel. If B = 3x + 16, g = 2x + 29 and a = 2y + 17 then find the values of X and Y the figure is not drawn to scale
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Y=
Since lines X and Y are parallel, their slopes are equal.
The equation of line X is given by B = 3x + 16.
Comparing this equation with the standard form y = mx + b, where m is the slope, we can see that the slope of line X is 3.
The equation of line Y is given by g = 2x + 29.
Comparing this equation with the standard form y = mx + b, where m is the slope, we can see that the slope of line Y is 2.
Since the slopes of X and Y are equal, we can equate them:
3 = 2
This equation is not true, which means there is no solution. Therefore, we cannot find the values of X and Y.
Since lines X and Y are parallel, they have the same slope.
The slope of line X can be found by comparing the coefficients of x and the constant term in equation B, which is 3x + 16. Therefore, the slope of line X is 3.
The slope of line Y can be found by comparing the coefficients of x and the constant term in equation g, which is 2x + 29. Therefore, the slope of line Y is 2.
Since lines X and Y have the same slope, we can set up the following equation:
3 = 2
However, this is not true. Therefore, there is no common solution for x and y that satisfies the condition of parallel lines.
To find the values of X and Y, we need to use the fact that lines X and Y are parallel. When two lines are parallel, the slopes of the lines are equal.
The slopes of lines X and Y are given by the coefficients of x in their respective equations. So, let's equate the slopes:
Slope of line X = Coefficient of x in B = 3
Slope of line Y = Coefficient of x in g = 2
Since lines X and Y are parallel, their slopes are equal. Therefore, 3 = 2.
Now we can solve this equation to find the value of x:
3 = 2x
Divide both sides by 2:
3/2 = x
Simplifying the fraction, we get:
x = 1.5
So, the value of x is 1.5.
To find the value of y, we can substitute the value of x into either equation B or g. Let's use equation B:
B = 3x + 16
Substituting x = 1.5:
B = 3(1.5) + 16
B = 4.5 + 16
B = 20.5
Now we have the value of B, which represents the y-intercept of line X.
Since lines X and Y are parallel, they have the same y-intercept. Therefore, the value of Y (y-intercept of line Y) is also 20.5.
So, the values of X and Y are:
X = 1.5
Y = 20.5