Respuesta :
2x - y = -2
x = 14 + 2y
Plug in the x equation
2(14+2y) - y = -2
Distribute
28 + 4y - y = -2
Combine variables
28 + 3y = -2
Subtract 28 on both sides
3y = -30
Divide the y
y = -10
x = 14 + 2y
Plug in the x equation
2(14+2y) - y = -2
Distribute
28 + 4y - y = -2
Combine variables
28 + 3y = -2
Subtract 28 on both sides
3y = -30
Divide the y
y = -10
ANSWER 1
The given system of equations is:
[tex]2x-y=-2[/tex]
[tex]x=14+2y[/tex]
Let us rewrite the second system to obtain,
[tex]2x-y=-2[/tex]
[tex]x-2y=14[/tex]
We need to apply the Cramer's rule. So we write out the coefficient matrices to obtain:
[tex]\left[\begin{array}{cc}2&-1\\1&-2\end{array}\right][/tex]
The answer column is;
[tex]\left[\begin{array}{c}-2&14\end{array}\right][/tex]
The value of the y-determinant is denoted by [tex]D_y[/tex]. To find this we replace the coefficient determinant with answer-column values in y-column to get,
[tex]D_y=\left|\begin{array}{cc}2&-2\\1&14\end{array}\right|[/tex]
Recall that,
If [tex]A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
then, [tex]det_{A}=\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-bc[/tex]
This implies that,
[tex]D_y=2\times14-1\times(-2)[/tex]
[tex]D_y=28+2[/tex]
[tex]D_y=30[/tex]
ANSWER 2
The value of the x-determinant is denoted by [tex]D_x[/tex]. To find this we replace the coefficient determinant with answer-column values in x-column to get,
[tex]D_x=\left|\begin{array}{cc}-2&-1\\14&-2\end{array}\right|[/tex]
This implies that,
[tex]D_x=-2\times-2-14\times-1[/tex]
[tex]D_x=4+14[/tex]
[tex]D_x=18[/tex]
ANSWER 3
To find the solution to the system of equations.
We need to find the determinant of the coefficient matrix.
[tex]D=\left|\begin{array}{cc}2&-1\\1&-2\end{array}\right|[/tex]
This implies that,
[tex]D=2\times(-2)-1\times-1[/tex]
[tex]D=-4+1[/tex]
[tex]D=-3[/tex]
Cramer's rule says that,
[tex]x=\frac{D_x}{D}[/tex]
[tex]\Rightarrow x=\frac{18}{-3}[/tex]
[tex]\Rightarrow x=-6[/tex]
and
[tex]y=\frac{D_y}{D}[/tex]
[tex]\Rightarrow y=\frac{30}{-3}[/tex]
[tex]\Rightarrow y=-10[/tex]
Therefore the solution is [tex]x=-6[/tex] and [tex]y=-10[/tex].
