What is the number value of k for which the system of linear equations (k+1) x+8y=4k & kx+(k+3) y=3k-1 has infinite solutions?
For solution to have infinite solutions, ratio of x coefficients=ratio of y coefficients=ratio of constants=>(k+1)/k=8/(k+3)=4k/(3k-1)solve (k+1)/k=8/(k+3)=>k^2+4k+3=8k=>k^2–4k+3=0=>k=1,3Now,8/(k+3)=4k/(3k-1)=>6k-2=k^2+3k=>k^2–3k+2=0=>k=1,2Now since both the conditions must be satisfied we take the value of k which satisfies both the equation hence k=1.
What is the value of x and y in simultaneous equations: 3x+4y=5 and 6x+8y=10?
There's no value for x and y. A solution to two simultaneous linear equations exist only if the two lines intersect. If you look at your given equations, they will not intersect as they are parallel lines. Thus, there's no solution.
What is the value of k for which the system of equation 2x+3y=7 and 8x+(k+4) y=0 has, infinitely, many solutions?
2x + 3y = 73y = -2x + 7y = (-2/3)x + 7/3 => slope = -2/3, y-intercept = 7/38x + (k + 4)y = 0(k + 4)y = -8xy = -8/(k + 4)x => slope = -8/(k + 4), y-intercept = 0, then the two lines can never coincide to have infinitely many solutions.-8/(k + 4) = -2/32k + 8 = 242k = 16k = 8 => for k = 8 the two lines will be parallel which means no solutions, no value of k will make them coincide:y = (-2/3)x + 7/3y = (-2/3)xDesmos graph
How many pairs of x and y satisfy the equations 6x+5y=16 and 8x+7y=22?
Well that depends on the fact whether they are forming a set of simultaneous linear equations here in the question or they are just two independent lines.Considering they are NOT a set of simultaneous linear equations, there would be infinite pairs of x and y which would satisfy the two independent lines.If they are in fact a set of simultaneous linear equations then : Both the equations represent two different lines with different slopes i.e. angle with x axis. So clearly they are neither parallel lines nor are they coincident lines. So they must intersect exactly at one point in the xy plane. Hence there would be only one pair of x and y satisfying this pair of simultaneous linear equations.
If 3x + 4y = 200 and 2x + 3y = 144, what are x and y?
6x + 8y = 400 (multiply first by 2)6x +9y = 432 (multiply second by 3)y = 32 (subtract first from second)x = (200 - 4*32)/3 = 24Why do we get this enormous amount of very simple math questions? Can’t Quora build a filter?