# Recent questions tagged coefficient-matrix

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How many real solutions are there to the system of equations?$y^2 = x^2 + 5x - 27$$x + 5 = y^2$
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Solve the equation $$x^2+2x+1=0$$. Use latex code for an WYSIWYG editor
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Solve the following system of equations:\left[\begin{array}{rrr}1 & 2 & 3 \\-1 & 4 & 2 \\3 & -6 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\ri... 472 views 1 answers How do you solve a system of linear equations using substitution? 308 views 0 answers Solve the system of equations 3x - 2y + z = 1, x + y + 2z = 2, and 2x - y + 3z = 3 using matrices. 549 views 0 answers Solve the system of equations x + 2y + 3z = 1, 2x + y + z = 2, and 3x + 2y + 2z = 3 using matrices. 357 views 0 answers Solve the system of equations 2x - y = 1 and x + 2y = 5 using matrices. 261 views 0 answers Solve the system of equations 3x + y = 5 and x - y = 1 using matrices. 355 views 0 answers Solve the system of equations 2x + 3y = 1 and x - 2y = 3 using matrices. 153 views 0 answers Solve \dfrac{x^2 + x - 6}{x^2 - 2x - 3} = 0 190 views 0 answers Solve \frac{x^2 + 2x + 3}{x^2 - 4} = 0 153 views 0 answers Solve \dfrac{2x^2 - 3x + 1}{x^2 + 1} = 0 394 views 0 answers Solve \begin{cases} x - y + 2z = 1 \\ 2x + 3y - z = 2 \\ 3x - 2y + 3z = 3 \end{cases} 277 views 0 answers Solve the equations \begin{cases} 2x + y + 3z = 2 \\ x - 2y + z = 3 \\ 3x + y - 2z = 1 \end{cases} 361 views 0 answers Solve \begin{cases} x + y - z = 0 \\ 2x - y + z = 1 \\ 3x + 2y - 2z = 2 \end{cases} 309 views 0 answers Solve the system of equations \begin{cases} 2x - y + 3z = 1 \\ x + 2y - z = 2 \\ 3x - y + 2z = 3 \end{cases} 244 views 0 answers Solve the simultaneous equation \begin{cases} x + y + z = 3 \\ x - y + 2z = 0 \\ 2x + 3y - z = 1 \end{cases} 193 views 0 answers Calculate the value of $$x$$ if $$2(3-x)=8$$. 198 views 0 answers Solve the simultaneous equations below:\[\begin{aligned}&3 x-y+z=5 \\&2 x+2 y+3 z=4 \\&x+3 y-z=11\end{aligned}
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The complex numbers $$z$$ and $$w$$ satisfy the simultaneous equations\begin{aligned}&2 z+\mathrm{i} w=-1 \\&z-w=3+3 \mathrm{i}\end{aligned}(a) Use algebra to find $$... 203 views 1 answers Show that \(\log _{2}(\sqrt[3]{5})=\frac{\log _{2} 5}{3}$$
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Show that $$\log \left(\frac{10}{100}\right)=\log 10-\log 100$$
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Show that $$\log (10 \cdot 100)=\log 10+\log 100$$.
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If $$\frac{\log x}{y-z}=\frac{\log y}{z-x}=\frac{\log z}{x-y}$$ then what is $$x^{x} \cdot y^{y} \cdot z^{z}$$
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Find the value of $$x$$$\log \left(98+\sqrt{x^{2}-12 x+36}\right)=2$
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Find the value of $$x$$, if$\sqrt{8^{0}+\frac{2}{3}}=(0.6)^{2-3 x}$
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Find $$x$$ and $$y$$, if\begin{aligned}&z^{3}=\sqrt{36^{5}}, y=x^{-5} \\&x=\log _{6} z-\frac{2}{3}\end{aligned}
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Find the solution to the following system.\begin{aligned}&x_{1}^{\prime}=x_{1}+2 x_{2} \quad x_{1}(0)=0 \\&x_{2}^{\prime}=3 x_{1}+2 x_{2} \quad x_{2}(0)=-4\end{aligned}... 254 views 1 answers Convert the following system to matrix form.\[\begin{aligned}&x_{1}^{\prime}=4 x_{1}+7 x_{2} \\&x_{2}^{\prime}=-2 x_{1}-5 x_{2}\end{aligned}
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Solve the simultaneous equations \begin{aligned} &x^{2}+y^{2}=49 \\ &y^{2}-5 x=49 \end{aligned}
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SOlve $$x(x-1)=20$$
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The HCF of $$12 x^{2} y ; 42 x^{3} y^{2} ; 27 x y$$ is:
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Consider the system of equations\begin{aligned}&x+y-z=a \\&x-y+2 z=b .\end{aligned}a) Find the general solution of the homogeneous equation, so $$a=b=0$$.b) A particu...
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Consider the system of linear equations$\begin{array}{rc}k x+y+z & =1 \\x+k y+z & =1 \\x+y+k z & =1\end{array}$For what value(s) of $$k$$ does this have (i) a unique so...
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Consider the system of equations\begin{aligned}&x+y-z=a \\&x-y+2 z=b .\end{aligned}a) Find the general solution of the homogeneous equation.b) A particular solution o...
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Solve the following system of equations.\begin{aligned}&x-y=2 \\&x+2 y=11 \\&-2 x+5 y=5\end{aligned}
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Solve the following system of equations.\begin{aligned}&x-3 y=-1 \\&x+y=7 \\&2 x+5 y=20\end{aligned}
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Solve the following system of equations. Let $$z$$ be the parameter.\begin{aligned}&x+2 y+3 z=1 \\&2 x+y-z=6\end{aligned}
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Solve the following system of equations. Let $$z$$ be the parameter.\begin{aligned}&x+3 y+6 z=19 \\&2 x-3 y+3 z=2\end{aligned}
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For the following system of equations, tell how many solutions there are in nonnegative integers.$\begin{array}{r}x+3 y+z=82 \\7 y+2 z=42\end{array}$
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For the following system of equations, tell how many solutions there are that are positive and result in $$z$$ being a positive integer.\begin{array}{r}x+2 y+z=88 \\7 y... 454 views 1 answers Solve the system of two equations in two unknowns.\[\begin{aligned}&2 x-3 y=5 \\&8 x-12 y=20\end{aligned}
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Solve the system of two equations in two unknowns.\begin{aligned}&5 x+6 y=1 \\&15 x+18 y=3\end{aligned}
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Solve the system of two equations in two unknowns.\begin{aligned}&y=5 x+2 \\&-10 x+2 y=1\end{aligned}
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Solve the system of two equations in two unknowns.\begin{aligned}&x=1-2 y \\&3 x+6 y=10\end{aligned}
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Solve the system of equations by the Substitution Method.\begin{aligned}&4 x-9 y=-1 \\&3 x+4 y=10\end{aligned}
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Solve the system of equations by the Substitution Method.\begin{aligned}&y=-2 x+3 \\&2 x-5 y=-51\end{aligned}
Solve the system of equations by the Substitution Method.\begin{aligned}&x=2 y+1 \\&4 x-3 y=14\end{aligned}
Solve the system of equations by graphing.\begin{aligned}&3 x-y=5 \\&4 x+y=2\end{aligned}
Consider a free particle in two dimensions confined by the boundary$$G:=\{(x, y):|x y|=1\} .$$Solve the eigenvalue problem$$\Delta \psi+k^{2} \psi=0$$wherek^{2}=\frac{2...