Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
2101	Solve by Substitution	x-y=2 , x-y=0	$x - y = 2$ , $x - y = 0$
2102	Solve by Substitution	x-y=3 , 2x-y=4	$x - y = 3$ , $2 x - y = 4$
2103	Solve by Substitution	x-y=4 , 7x+8y=-107	$x - y = 4$ , $7 x + 8 y = - 107$
2104	Solve Using an Inverse Matrix	y=-0.5x-4 , y=x+1	$y = - 0.5 x - 4$ , $y = x + 1$
2105	Solve Using a Matrix with Cramer's Rule	y+x=-2 , 3+x=3-2y	$y + x = - 2$ , $3 + x = 3 - 2 y$
2106	Solve Using a Matrix with Cramer's Rule	x+y=-4 , y=-3-x-3	$x + y = - 4$ , $y = - 3 - x - 3$
2107	Find the Intersection of the Inequalities	y+5x=0 , 3x-2y=6	$y + 5 x = 0$ , $3 x - 2 y = 6$
2108	Find the Quadrant	(1.2,3.6)	$(1.2, 3.6)$
2109	Find the Slope	(2,-5) , (4,-6)	$(2, - 5) (4, - 6)$
2110	Expand the Logarithmic Expression	log base 6 of (ab^4)/( cube root of c^2)	$\log_{6} (\frac{a b^{4}}{\sqrt[3]{c^{2}}})$
2111	Graph	3 log base 3 of x- log base 3 of y	$3 \log_{3} (x) - \log_{3} (y)$
2112	Find the Power Set	(2,4)	$(2, 4)$
2113	Solve Using a Matrix by Elimination	2a+b-g=4 , b+g+h=4 , a-d+2g=0	$2 a + b - g = 4$ , $b + g + h = 4$ , $a - d + 2 g = 0$
2114	Solve Using a Matrix by Elimination	5x+3=4y , y=8x-2	$5 x + 3 = 4 y$ , $y = 8 x - 2$
2115	Solve Using a Matrix by Elimination	x=7(y-5) , 4y=3x+5	$x = 7 (y - 5)$ , $4 y = 3 x + 5$
2116	Solve Using a Matrix by Elimination	(3)^2a+3b+c=4 , (5)^2a+5b+c=4 , (2)^2a+2b+c=1	${(3)}^{2} a + 3 b + c = 4$ , ${(5)}^{2} a + 5 b + c = 4$ , ${(2)}^{2} a + 2 b + c = 1$
2117	Solve Using a Matrix by Elimination	1/(x-5)-3/(x+6)=0 , 3/(x+7)-1/(y-3)=0	$\frac{1}{x - 5} - \frac{3}{x + 6} = 0$ , $\frac{3}{x + 7} - \frac{1}{y - 3} = 0$
2118	Solve Using a Matrix by Elimination	3^2a+3b+c=4 , 5^2a+5b+c=4 , 2^2a+2b+c=1	$3^{2} a + 3 b + c = 4$ , $5^{2} a + 5 b + c = 4$ , $2^{2} a + 2 b + c = 1$
2119	Solve Using a Matrix by Elimination	0.15g-0.35h=-0.5 , -0.012g+0.25h=0.1	$0.15 g - 0.35 h = - 0.5$ , $- 0.012 g + 0.25 h = 0.1$
2120	Solve Using a Matrix by Elimination	2a-2b=0 , d+3g=2 , 3a-3b=0 , a-b+2d+6g=4	$2 a - 2 b = 0$ , $d + 3 g = 2$ , $3 a - 3 b = 0$ , $a - b + 2 d + 6 g = 4$
2121	Solve Using a Matrix by Elimination	2x+y-z=2 , x+3y+2z=1 , x+y+z=2	$2 x + y - z = 2$ , $x + 3 y + 2 z = 1$ , $x + y + z = 2$
2122	Solve Using a Matrix by Elimination	2x+y-z=5 , x+4y+2z=16 , 15x+6y-2z=12	$2 x + y - z = 5$ , $x + 4 y + 2 z = 16$ , $15 x + 6 y - 2 z = 12$
2123	Solve Using a Matrix by Elimination	2x-12y-4z=5 , x+7y-z=-4 , x+3y=7	$2 x - 12 y - 4 z = 5$ , $x + 7 y - z = - 4$ , $x + 3 y = 7$
2124	Solve Using a Matrix by Elimination	2x-8y-z=-23 , x+9y-9z=-36 , 6x+y+z=67	$2 x - 8 y - z = - 23$ , $x + 9 y - 9 z = - 36$ , $6 x + y + z = 67$
2125	Solve Using a Matrix by Elimination	3a+5b+2d=0 , 4a+7b+5d=0 , a+b-4d=0 , 2a+9b+6d=0	$3 a + 5 b + 2 d = 0$ , $4 a + 7 b + 5 d = 0$ , $a + b - 4 d = 0$ , $2 a + 9 b + 6 d = 0$
2126	Solve Using a Matrix by Elimination	3x+2y+6z=5 , 6x+3y+7z=8 , 4x+5y-7z=10	$3 x + 2 y + 6 z = 5$ , $6 x + 3 y + 7 z = 8$ , $4 x + 5 y - 7 z = 10$
2127	Solve Using a Matrix by Elimination	-3x-5y+z=3 , 5x+y-6z=2 , x+4y+z=-6	$- 3 x - 5 y + z = 3$ , $5 x + y - 6 z = 2$ , $x + 4 y + z = - 6$
2128	Solve Using a Matrix by Elimination	3y+2z=2 , 2x-y-3z=2 , 2x+2y-z=4	$3 y + 2 z = 2$ , $2 x - y - 3 z = 2$ , $2 x + 2 y - z = 4$
2129	Solve Using a Matrix by Elimination	4x-y+3z=-8 , x-8y+5z=3 , 2y-7z=-4	$4 x - y + 3 z = - 8$ , $x - 8 y + 5 z = 3$ , $2 y - 7 z = - 4$
2130	Solve Using a Matrix by Elimination	52f+48b+36m=67936 , f-b-m=398 , b-3m=453	$52 f + 48 b + 36 m = 67936$ , $f - b - m = 398$ , $b - 3 m = 453$
2131	Solve Using a Matrix by Elimination	5a+3b+d=90 , 2a+4b+g=64	$5 a + 3 b + d = 90$ , $2 a + 4 b + g = 64$
2132	Solve Using a Matrix by Elimination	-5a-30b+5d=-10 , a+4b-5d=6 , -a-4b+9d=-3	$- 5 a - 30 b + 5 d = - 10$ , $a + 4 b - 5 d = 6$ , $- a - 4 b + 9 d = - 3$
2133	Solve Using a Matrix by Elimination	5x+4y-5z=4 , 3x-5y+3z=1 , 6x-2y+6z=10	$5 x + 4 y - 5 z = 4$ , $3 x - 5 y + 3 z = 1$ , $6 x - 2 y + 6 z = 10$
2134	Solve Using a Matrix by Elimination	7x-5y-z=18 , x-2y-5z=-33 , -4x+y+z=-17	$7 x - 5 y - z = 18$ , $x - 2 y - 5 z = - 33$ , $- 4 x + y + z = - 17$
2135	Solve Using a Matrix by Elimination	-8x+6y-4z=2 , -2x-6y+7z=24 , -6x+12y+5z=10	$- 8 x + 6 y - 4 z = 2$ , $- 2 x - 6 y + 7 z = 24$ , $- 6 x + 12 y + 5 z = 10$
2136	Solve Using a Matrix by Elimination	9c-3d=-33 , 6c+5d=-8	$9 c - 3 d = - 33$ , $6 c + 5 d = - 8$
2137	Solve Using a Matrix by Elimination	-a+5b=12 , -a-3b=10	$- a + 5 b = 12$ , $- a - 3 b = 10$
2138	Solve Using a Matrix by Elimination	a+2b+4d=13 , -a+b+2d=2 , 4a+10b+12d=46	$a + 2 b + 4 d = 13$ , $- a + b + 2 d = 2$ , $4 a + 10 b + 12 d = 46$
2139	Solve Using a Matrix by Elimination	a+2b+g=7 , a+b+d-g=3 , 3a+b+5d-7g=1	$a + 2 b + g = 7$ , $a + b + d - g = 3$ , $3 a + b + 5 d - 7 g = 1$
2140	Solve Using a Matrix by Elimination	a+2b=4 , -2a+4b=-8	$a + 2 b = 4$ , $- 2 a + 4 b = - 8$
2141	Solve Using a Matrix by Elimination	a+3b=1 , 3a-2b=14	$a + 3 b = 1$ , $3 a - 2 b = 14$
2142	Solve Using a Matrix by Elimination	x+2y-z=-3 , 2x-4y+z=-7 , -2x+2y-3z=4	$x + 2 y - z = - 3$ , $2 x - 4 y + z = - 7$ , $- 2 x + 2 y - 3 z = 4$
2143	Solve Using a Matrix by Elimination	x+y+2z=-1 , x+3y-6z=5 , 2x+5y-8z=7	$x + y + 2 z = - 1$ , $x + 3 y - 6 z = 5$ , $2 x + 5 y - 8 z = 7$
2144	Solve Using a Matrix by Elimination	x+y+z=-4 , x-y+4z=6 , 4x+y+z=-16	$x + y + z = - 4$ , $x - y + 4 z = 6$ , $4 x + y + z = - 16$
2145	Solve Using a Matrix by Elimination	x+y+z=6 , 2x-y+3z=8 , x+2y=4	$x + y + z = 6$ , $2 x - y + 3 z = 8$ , $x + 2 y = 4$
2146	Solve Using a Matrix by Elimination	x+y-z=2 , x+2y+3z=7 , x+3y-z=4	$x + y - z = 2$ , $x + 2 y + 3 z = 7$ , $x + 3 y - z = 4$
2147	Solve Using a Matrix by Elimination	x-2y+3x=9 , -x+3y=-4 , 2x-5y+5z=17	$x - 2 y + 3 x = 9$ , $- x + 3 y = - 4$ , $2 x - 5 y + 5 z = 17$
2148	Solve Using a Matrix by Elimination	-x-2y-2z=-3 , -x-5y-2z=-9 , -x-5y-5z=-6	$- x - 2 y - 2 z = - 3$ , $- x - 5 y - 2 z = - 9$ , $- x - 5 y - 5 z = - 6$
2149	Solve Using a Matrix by Elimination	x-3y+3z=-6 , 4x+y-z=-11 , 3x+4y-5z=-8	$x - 3 y + 3 z = - 6$ , $4 x + y - z = - 11$ , $3 x + 4 y - 5 z = - 8$
2150	Solve Using a Matrix by Elimination	x-4y+2z=8 , -2x+y-7z=0 , -7y-3z=16	$x - 4 y + 2 z = 8$ , $- 2 x + y - 7 z = 0$ , $- 7 y - 3 z = 16$
2151	Solve Using a Matrix by Elimination	x-5y-z=10 , -x+7y-z=18 , 5x-4y-2z=-14	$x - 5 y - z = 10$ , $- x + 7 y - z = 18$ , $5 x - 4 y - 2 z = - 14$
2152	Solve Using a Matrix by Elimination	x-7y+7z=-27 , -6x+y+8z=-38 , 2x+3y+7z=-26	$x - 7 y + 7 z = - 27$ , $- 6 x + y + 8 z = - 38$ , $2 x + 3 y + 7 z = - 26$
2153	Solve Using a Matrix by Elimination	x-y+4z=6 , 2x+y+z=1 , x+5y+z=-9	$x - y + 4 z = 6$ , $2 x + y + z = 1$ , $x + 5 y + z = - 9$
2154	Solve Using a Matrix by Elimination	x-y+z=3 , x+2y+3z=17 , 2x+3y-4z=-8	$x - y + z = 3$ , $x + 2 y + 3 z = 17$ , $2 x + 3 y - 4 z = - 8$
2155	Solve Using an Augmented Matrix	-2a+3b=15 , 4/3a+2=-2b	$- 2 a + 3 b = 15$ , $\frac{4}{3} a + 2 = - 2 b$
2156	Write as a Vector Equality	1/5x+3/10y=1 , 1/6x-1/3y=2	$\frac{1}{5} x + \frac{3}{10} y = 1$ , $\frac{1}{6} x - \frac{1}{3} y = 2$
2157	Write as a Vector Equality	2/x-3/y=2 , -10/x+9/y=-8	$\frac{2}{x} - \frac{3}{y} = 2$ , $- \frac{10}{x} + \frac{9}{y} = - 8$
2158	Write as a Vector Equality	p^2+4h^2=4 , h=p+1	$p^{2} + 4 h^{2} = 4$ , $h = p + 1$
2159	Write as a Vector Equality	square root of 4-5x=2x-1 , square root of 4-5x=2x-1	$\sqrt{4 - 5 x} = 2 x - 1$ , $\sqrt{4 - 5 x} = 2 x - 1$
2160	Write as a Vector Equality	x^2-y^2=48 , x^2-xy-2y^2=40	$x^{2} - y^{2} = 48$ , $x^{2} - x y - 2 y^{2} = 40$
2161	Write as a Vector Equality	x^2+y^2=25 , (x^2)/(5^2)-(y^2)/(5^2)=1	$x^{2} + y^{2} = 25$ , $\frac{x^{2}}{5^{2}} - \frac{y^{2}}{5^{2}} = 1$
2162	Write as a Vector Equality	x^2+y^2=100 , y=-x-2	$x^{2} + y^{2} = 100$ , $y = - x - 2$
2163	Write as a Vector Equality	-0.2x-0.7y=0.21 , 0.9x+0.8y=0.23	$- 0.2 x - 0.7 y = 0.21$ , $0.9 x + 0.8 y = 0.23$
2164	Write as a Vector Equality	10+8y=-10 , -8x-8y=-8	$10 + 8 y = - 10$ , $- 8 x - 8 y = - 8$
2165	Write as a Vector Equality	12x=240 , 12x-18=240	$12 x = 240$ , $12 x - 18 = 240$
2166	Write as a Vector Equality	13x-6y=10 , 26x-12y=15	$13 x - 6 y = 10$ , $26 x - 12 y = 15$
2167	Write as a Vector Equality	1575=(x+y)4.5 , 1575=(x+y)3.5	$1575 = (x + y) \cdot 4.5$ , $1575 = (x + y) \cdot 3.5$
2168	Write as a Vector Equality	-18x+6y=24 , 3x-y=-2	$- 18 x + 6 y = 24$ , $3 x - y = - 2$
2169	Write as a Vector Equality	2a+b=7 , 3a+1.5=21	$2 a + b = 7$ , $3 a + 1.5 = 21$
2170	Write as a Vector Equality	2p+3q=1 , p+4q=3	$2 p + 3 q = 1$ , $p + 4 q = 3$
2171	Write as a Vector Equality	2x+2y=190 , x-y=25	$2 x + 2 y = 190$ , $x - y = 25$
2172	Write as a Vector Equality	-2x+2y-10z=-6 , x-y+5z=3 , 5x-5y+25z=15	$- 2 x + 2 y - 10 z = - 6$ , $x - y + 5 z = 3$ , $5 x - 5 y + 25 z = 15$
2173	Write as a Vector Equality	2x+3y=6 , 8x+12y=0	$2 x + 3 y = 6$ , $8 x + 12 y = 0$
2174	Write as a Vector Equality	2x+3y-4z=-13 , -x+3y+2z=-7 , 3x-2y+z=14	$2 x + 3 y - 4 z = - 13$ , $- x + 3 y + 2 z = - 7$ , $3 x - 2 y + z = 14$
2175	Write as a Vector Equality	2x+3y-z=-1 , 6x+9y-3z=-3 , -2x-3y+2z=1	$2 x + 3 y - z = - 1$ , $6 x + 9 y - 3 z = - 3$ , $- 2 x - 3 y + 2 z = 1$
2176	Write as a Vector Equality	2x+3y-z=6 , x-2y+z=-1 , 3x+y-3z=-1	$2 x + 3 y - z = 6$ , $x - 2 y + z = - 1$ , $3 x + y - 3 z = - 1$
2177	Write as a Vector Equality	2x+4y-2z=-14 , x+2y+4z=3 , x+2y-z=-7	$2 x + 4 y - 2 z = - 14$ , $x + 2 y + 4 z = 3$ , $x + 2 y - z = - 7$
2178	Write as a Vector Equality	2x+6y-4z=0 , -3x-9y+8z=0 , -x-2y+z=0	$2 x + 6 y - 4 z = 0$ , $- 3 x - 9 y + 8 z = 0$ , $- x - 2 y + z = 0$
2179	Find the Domain	v	$v$
2180	Find the Domain	-3x+2y=2	$- 3 x + 2 y = 2$
2181	Find the Inverse	[[-1,1],[1,-2]]	$[\begin{array}{c} - 1 & 1 \\ 1 & - 2 \end{array}]$
2182	Find the Derivative - d/dx	f(x)=x^2-2x-3	$f (x) = x^{2} - 2 x - 3$
2183	Cancel the Common Factors	(x-3x^2+2)÷(x-3)	$(x - 3 x^{2} + 2) \div (x - 3)$
2184	Find the Roots (Zeros)	-5k^2-k+5=9	$- 5 k^{2} - k + 5 = 9$
2185	Find the Roots (Zeros)	f(x)=5x^6+x^2 log of x+x	$f (x) = 5 x^{6} + x^{2} \log (x + x)$
2186	Solve Using the Quadratic Formula	1.3=(4.2)t+0.5(-9.8)t^2	$1.3 = (4.2) t + 0.5 (- 9.8) t^{2}$
2187	Find the Derivative - d/dx	4x-y=17	$4 x - y = 17$
2188	Write as a Function of z	z^3+(1+i)z^2+(6+i)z+6=0	$z^{3} + (1 + i) z^{2} + (6 + i) z + 6 = 0$
2189	Find the Range	y=1/3x	$y = \frac{1}{3} x$
2190	Find the Asymptotes	f(x)=((x-2)(x-4))/((x-4)(x+1))	$f (x) = \frac{(x - 2) (x - 4)}{(x - 4) (x + 1)}$
2191	Simplify	(4w^3-2w^2)*(10w^4)	$(4 w^{3} - 2 w^{2}) \cdot (10 w^{4})$
2192	Factor	x^2(b-c)+b^2(c+x)-c^2(x+b)	$x^{2} (b - c) + b^{2} (c + x) - c^{2} (x + b)$
2193	Factor	11x+55y	$11 x + 55 y$
2194	Factor	11x-2	$11 x - 2$
2195	Factor	4x^2+2x-3	$4 x^{2} + 2 x - 3$
2196	Factor	6w^2-7w+1	$6 w^{2} - 7 w + 1$
2197	Factor	8xy-4*(2y^2)	$8 x y - 4 \cdot (2 y^{2})$
2198	Evaluate Using the Given Value	f(1)=23/6	$f (1) = \frac{23}{6}$
2199	Evaluate Using the Given Value	y=2^x , 2^2.3	$y = 2^{x}$ , $2^{2.3}$
2200	Add	3a^2+2ab-3b^2 , 4a^2-9b-4b^2	$3 a^{2} + 2 a b - 3 b^{2}$ , $4 a^{2} - 9 b - 4 b^{2}$