Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2001	Write as a Vector Equality	x^2-4y=0 , x-y=0	$x^{2} - 4 y = 0$ , $x - y = 0$
2002	Write as a Vector Equality	x^2-xy+y^2=21 , x^2-2xy-8y^2=0	$x^{2} - x y + y^{2} = 21$ , $x^{2} - 2 x y - 8 y^{2} = 0$
2003	Write as a Vector Equality	x^2-y=0 , 6x+y=7	$x^{2} - y = 0$ , $6 x + y = 7$
2004	Write as a Vector Equality	(x+2)/6-(y+6)/3+z/2=0 , (x+1)/2+(y-1)/2-z/4=6 , (x-5)/4+(y+1)/3+(z-2)/2=83/12	$\frac{x + 2}{6} - \frac{y + 6}{3} + \frac{z}{2} = 0$ , $\frac{x + 1}{2} + \frac{y - 1}{2} - \frac{z}{4} = 6$ , $\frac{x - 5}{4} + \frac{y + 1}{3} + \frac{z - 2}{2} = \frac{83}{12}$
2005	Write as a Vector Equality	(x+5)/2-(y+5)/3=4 , (x+y)/2=1/3+(x-y)/3	$\frac{x + 5}{2} - \frac{y + 5}{3} = 4$ , $\frac{x + y}{2} = \frac{1}{3} + \frac{x - y}{3}$
2006	Write as a Vector Equality	(x+y)/7=(y+4)/5 , (x-z)/5=(y-4)/2 , (y-z)/3=(x+2)/10	$\frac{x + y}{7} = \frac{y + 4}{5}$ , $\frac{x - z}{5} = \frac{y - 4}{2}$ , $\frac{y - z}{3} = \frac{x + 2}{10}$
2007	Write as a Vector Equality	y^2=(x^2-9) , (x-3)^2+(y+3)^2=9	$y^{2} = (x^{2} - 9)$ , ${(x - 3)}^{2} + {(y + 3)}^{2} = 9$
2008	Write as a Vector Equality	0.05x+0.04y=273 , x=2y	$0.05 x + 0.04 y = 273$ , $x = 2 y$
2009	Write as a Vector Equality	0.1x+0.4=-0.4 , 0.7x-0.7y=7.7	$0.1 x + 0.4 = - 0.4$ , $0.7 x - 0.7 y = 7.7$
2010	Write as a Vector Equality	0.5+4y=-1 , x+2.5y=3.5	$0.5 + 4 y = - 1$ , $x + 2.5 y = 3.5$
2011	Write as a Vector Equality	0.6x+3.6y=-12 , -0.9+0.6=6	$0.6 x + 3.6 y = - 12$ , $- 0.9 + 0.6 = 6$
2012	Write as a Vector Equality	1.3x+2.4y=-39.3 , 0.6x+0.3y=-3.6	$1.3 x + 2.4 y = - 39.3$ , $0.6 x + 0.3 y = - 3.6$
2013	Write as a Vector Equality	1.5x-2.0y=-1.0 , 3.0x+2.5y=3.2	$1.5 x - 2 y = - 1$ , $3 x + 2.5 y = 3.2$
2014	Write as a Vector Equality	1+1-1+1=1 , 3+4+1-3=-8 , 3+1-1-1=-15 , -1+2+1-3=-2	$1 + 1 - 1 + 1 = 1$ , $3 + 4 + 1 - 3 = - 8$ , $3 + 1 - 1 - 1 = - 15$ , $- 1 + 2 + 1 - 3 = - 2$
2015	Write as a Vector Equality	1=a^0+a+a^2 , 2=a^0+a2+a^24 , 3=a^0+a3+a^29	$1 = a^{0} + a + a^{2}$ , $2 = a^{0} + a \cdot 2 + a^{2} \cdot 4$ , $3 = a^{0} + a \cdot 3 + a^{2} \cdot 9$
2016	Write as a Vector Equality	10t^3p=2375 , 11t+4p=270	$10 t^{3} p = 2375$ , $11 t + 4 p = 270$
2017	Write as a Vector Equality	10=d , 7=a+b+c+d , -11=27a+9b+3c+d , -14=64a+16b+4c+d	$10 = d$ , $7 = a + b + c + d$ , $- 11 = 27 a + 9 b + 3 c + d$ , $- 14 = 64 a + 16 b + 4 c + d$
2018	Write as a Vector Equality	10x+18y=-11 , 16x-9y=-5	$10 x + 18 y = - 11$ , $16 x - 9 y = - 5$
2019	Write as a Vector Equality	10x+2y=6 , -25x+ky=-14	$10 x + 2 y = 6$ , $- 25 x + k y = - 14$
2020	Write as a Vector Equality	10x+2y=-6 , y=-5x	$10 x + 2 y = - 6$ , $y = - 5 x$
2021	Write as a Vector Equality	10x=40 , 20x=70 , 35x=P	$10 x = 40$ , $20 x = 70$ , $35 x = P$
2022	Write as a Vector Equality	10x-2y+5x=-1 , 6x-y+4z=-2 , x+z=3	$10 x - 2 y + 5 x = - 1$ , $6 x - y + 4 z = - 2$ , $x + z = 3$
2023	Write as a Vector Equality	11x+15y+23=0 , 7x-2y-20=0	$11 x + 15 y + 23 = 0$ , $7 x - 2 y - 20 = 0$
2024	Write as a Vector Equality	11x+7y+2z=1780 , 14x+8y+3z=2220 , x+y+z=300	$11 x + 7 y + 2 z = 1780$ , $14 x + 8 y + 3 z = 2220$ , $x + y + z = 300$
2025	Write as a Vector Equality	12x+5y+6=0 , (5x)/3-(7y)/6=-12	$12 x + 5 y + 6 = 0$ , $\frac{5 x}{3} - \frac{7 y}{6} = - 12$
2026	Write as a Vector Equality	14x-21y+14z=2 , -21x+14y+7z=2	$14 x - 21 y + 14 z = 2$ , $- 21 x + 14 y + 7 z = 2$
2027	Write as a Vector Equality	14x-28y=-22 , x+y=1	$14 x - 28 y = - 22$ , $x + y = 1$
2028	Write as a Vector Equality	15x-10y=5 , 15y=-5+10x	$15 x - 10 y = 5$ , $15 y = - 5 + 10 x$
2029	Write as a Vector Equality	15x-20y=-7 , 10y=4+10x	$15 x - 20 y = - 7$ , $10 y = 4 + 10 x$
2030	Write as a Vector Equality	16x-10y=6 , 8x-5y=3	$16 x - 10 y = 6$ , $8 x - 5 y = 3$
2031	Write as a Vector Equality	17x-5y=4 , 2x+7y=46	$17 x - 5 y = 4$ , $2 x + 7 y = 46$
2032	Write as a Vector Equality	-1x+0y+z=0 , x+y+0z=-3 , 0x+y+3z=1	$- 1 x + 0 y + z = 0$ , $x + y + 0 z = - 3$ , $0 x + y + 3 z = 1$
2033	Write as a Vector Equality	1x+2y=4 , 3x+36=48	$1 x + 2 y = 4$ , $3 x + 36 = 48$
2034	Write as a Vector Equality	-2+y=-1 , 4x-2y=-2	$- 2 + y = - 1$ , $4 x - 2 y = - 2$
2035	Write as a Vector Equality	288=75x+85x , 288=100x	$288 = 75 x + 85 x$ , $288 = 100 x$
2036	Write as a Vector Equality	2a+4b=20 , a^2-26=5b	$2 a + 4 b = 20$ , $a^{2} - 26 = 5 b$
2037	Write as a Vector Equality	2a+d=24 , 2b+d=17 , 2a+2b=x	$2 a + d = 24$ , $2 b + d = 17$ , $2 a + 2 b = x$
2038	Write as a Vector Equality	2r+s=3 , 4r+s=7 , 2r+5s=-1	$2 r + s = 3$ , $4 r + s = 7$ , $2 r + 5 s = - 1$
2039	Write as a Vector Equality	2w+3x-y-z=9 , w+x-y-z=0 , 6w+x-2y-z=4 , -w+2x+3y-z=5	$2 w + 3 x - y - z = 9$ , $w + x - y - z = 0$ , $6 w + x - 2 y - z = 4$ , $- w + 2 x + 3 y - z = 5$
2040	Write as a Vector Equality	2x+3y=11 , -2x+5y=13	$2 x + 3 y = 11$ , $- 2 x + 5 y = 13$
2041	Write as a Vector Equality	2a+3b-3d=0 , a+2b+d=3 , a+3b+3d=7	$2 a + 3 b - 3 d = 0$ , $a + 2 b + d = 3$ , $a + 3 b + 3 d = 7$
2042	Solve by Substitution	40x+y=19200 , 60x+y=19200	$40 x + y = 19200$ , $60 x + y = 19200$
2043	Solve by Substitution	4x+11=-6y , 6x+9y=-3	$4 x + 11 = - 6 y$ , $6 x + 9 y = - 3$
2044	Solve by Substitution	4x+2y=12 , x+2y=6	$4 x + 2 y = 12$ , $x + 2 y = 6$
2045	Solve by Substitution	4x+3y+7=0 , 5x-2y+3=0	$4 x + 3 y + 7 = 0$ , $5 x - 2 y + 3 = 0$
2046	Solve by Substitution	4x+3y=0 , 16x+4=6y	$4 x + 3 y = 0$ , $16 x + 4 = 6 y$
2047	Solve by Substitution	4x+3y=-10 , 3x+2y=-6	$4 x + 3 y = - 10$ , $3 x + 2 y = - 6$
2048	Solve by Substitution	4x+3y=85 , 3x+5y=115	$4 x + 3 y = 85$ , $3 x + 5 y = 115$
2049	Solve by Substitution	4x+4y=5 , 2x-8y=-5	$4 x + 4 y = 5$ , $2 x - 8 y = - 5$
2050	Solve by Substitution	4x+7y=15 , 6x-5y=21	$4 x + 7 y = 15$ , $6 x - 5 y = 21$
2051	Solve by Substitution	4x-10y=6 , 4x-3y=-5	$4 x - 10 y = 6$ , $4 x - 3 y = - 5$
2052	Solve by Substitution	4x-5y=-17 , 3x+2y=-7	$4 x - 5 y = - 17$ , $3 x + 2 y = - 7$
2053	Solve by Substitution	4x-7y=13 , x+9y=5	$4 x - 7 y = 13$ , $x + 9 y = 5$
2054	Solve by Substitution	4x-y=6 , 9x-2y=14	$4 x - y = 6$ , $9 x - 2 y = 14$
2055	Solve by Substitution	5x+3y=4 , 5x+y=9	$5 x + 3 y = 4$ , $5 x + y = 9$
2056	Solve by Substitution	5x+3y=-7 , 7x-3y=55	$5 x + 3 y = - 7$ , $7 x - 3 y = 55$
2057	Solve by Substitution	-5x+5y=15 , -2x+y=-3	$- 5 x + 5 y = 15$ , $- 2 x + y = - 3$
2058	Solve by Substitution	5x+6y=100 , 2x+3y=46	$5 x + 6 y = 100$ , $2 x + 3 y = 46$
2059	Solve by Substitution	-5x+y=-12 , -10x+5y=-15	$- 5 x + y = - 12$ , $- 10 x + 5 y = - 15$
2060	Solve by Substitution	-5x+y=-12 , -5x+y=26	$- 5 x + y = - 12$ , $- 5 x + y = 26$
2061	Solve by Substitution	5x-5y=-20 , -7x+5y=10	$5 x - 5 y = - 20$ , $- 7 x + 5 y = 10$
2062	Solve by Substitution	5x-y=19 , x+9y=59	$5 x - y = 19$ , $x + 9 y = 59$
2063	Solve by Substitution	5x-y=-4 , -2x+y=1	$5 x - y = - 4$ , $- 2 x + y = 1$
2064	Solve by Substitution	65x+70y=643 , x+y=950	$65 x + 70 y = 643$ , $x + y = 950$
2065	Solve by Substitution	6x-4y=30 , 12x+5y=-18	$6 x - 4 y = 30$ , $12 x + 5 y = - 18$
2066	Solve by Substitution	6x-4y=-44 , 2x+3y=-6	$6 x - 4 y = - 44$ , $2 x + 3 y = - 6$
2067	Solve by Substitution	6x-y=5 , 3x+y=4	$6 x - y = 5$ , $3 x + y = 4$
2068	Solve by Substitution	8x+2y=-6 , -6x+y=17	$8 x + 2 y = - 6$ , $- 6 x + y = 17$
2069	Solve by Substitution	-8x+3y=-33 , 5x+y=35	$- 8 x + 3 y = - 33$ , $5 x + y = 35$
2070	Solve by Substitution	8x+y=11 , -3x+3y=-21	$8 x + y = 11$ , $- 3 x + 3 y = - 21$
2071	Solve by Substitution	-8x-10y=24 , 6x+5y=2	$- 8 x - 10 y = 24$ , $6 x + 5 y = 2$
2072	Solve by Substitution	8x-5y=-10 , -x-5y=11	$8 x - 5 y = - 10$ , $- x - 5 y = 11$
2073	Solve by Substitution	8x-6y=-20 , -16x+7y=30	$8 x - 6 y = - 20$ , $- 16 x + 7 y = 30$
2074	Solve by Substitution	x+14y=2 , 2x+7y=-8	$x + 14 y = 2$ , $2 x + 7 y = - 8$
2075	Solve by Substitution	x+2y=1 , 4x+5y=13	$x + 2 y = 1$ , $4 x + 5 y = 13$
2076	Solve by Substitution	x+2y=-1 , 3x+5y=-6	$x + 2 y = - 1$ , $3 x + 5 y = - 6$
2077	Solve by Substitution	x+2y=2 , -x-2y+2=0	$x + 2 y = 2$ , $- x - 2 y + 2 = 0$
2078	Solve by Substitution	x+2y=5 , x-4y=-7	$x + 2 y = 5$ , $x - 4 y = - 7$
2079	Solve by Substitution	x+3y=15 , 4x+y=6	$x + 3 y = 15$ , $4 x + y = 6$
2080	Solve by Substitution	x+3y=15 , x+y=5	$x + 3 y = 15$ , $x + y = 5$
2081	Solve by Substitution	x+3y=2 , 3x+9y=6	$x + 3 y = 2$ , $3 x + 9 y = 6$
2082	Solve by Substitution	-x+3y-3=0 , x-3y=3	$- x + 3 y - 3 = 0$ , $x - 3 y = 3$
2083	Solve by Substitution	x+4y=4 , -x-4y+4=0	$x + 4 y = 4$ , $- x - 4 y + 4 = 0$
2084	Solve by Substitution	x+4y-8=0 , -x-4y=8	$x + 4 y - 8 = 0$ , $- x - 4 y = 8$
2085	Solve by Substitution	x+5y=4 , 6x-5y=3	$x + 5 y = 4$ , $6 x - 5 y = 3$
2086	Solve by Substitution	x+7y=5 , 4x+8y=-20	$x + 7 y = 5$ , $4 x + 8 y = - 20$
2087	Solve by Substitution	x+y=0 , 3x+y=4	$x + y = 0$ , $3 x + y = 4$
2088	Solve by Substitution	x+y=-10 , (x+3)^2+(y+9)^2=10	$x + y = - 10$ , ${(x + 3)}^{2} + {(y + 9)}^{2} = 10$
2089	Solve by Substitution	x+y=160 , 10x+15y=1825	$x + y = 160$ , $10 x + 15 y = 1825$
2090	Solve by Substitution	x+y=2 , 2x+2y=-6	$x + y = 2$ , $2 x + 2 y = - 6$
2091	Solve by Substitution	x+y=85 , 0.25x+0.05y=11.25	$x + y = 85$ , $0.25 x + 0.05 y = 11.25$
2092	Solve by Substitution	x-2y=-1 , 2x+y=4	$x - 2 y = - 1$ , $2 x + y = 4$
2093	Solve by Substitution	x-2y=-28 , x-y=-8	$x - 2 y = - 28$ , $x - y = - 8$
2094	Solve by Substitution	x-2y=6 , 2x+y=2	$x - 2 y = 6$ , $2 x + y = 2$
2095	Solve by Substitution	-x-2y=-8 , x+2y+8=0	$- x - 2 y = - 8$ , $x + 2 y + 8 = 0$
2096	Solve by Substitution	-x-3y=6 , x+3y=6	$- x - 3 y = 6$ , $x + 3 y = 6$
2097	Solve by Substitution	x-3y=8 , -2x+3y=-7	$x - 3 y = 8$ , $- 2 x + 3 y = - 7$
2098	Solve by Substitution	x-4y=-16 , -4x-6y=-2	$x - 4 y = - 16$ , $- 4 x - 6 y = - 2$
2099	Solve by Substitution	x-5y=5 , -x-5y=5	$x - 5 y = 5$ , $- x - 5 y = 5$
2100	Solve by Substitution	x-y=1 , 4x-4y=4	$x - y = 1$ , $4 x - 4 y = 4$