Question

Solve the equation:

[3 2
5 5]

[x1
x2]+
[1
2]=
[2
-3]

Answer 1

9514 1404 393

Answer:

(x1, x2) = (3, -4)

Explanation:

As with any 2-step linear equation, subtract the constant, then multiply by the inverse of the coefficient of the variable.

`\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]+\left[\begin{array}{c}1\\2\end{array}\right]=\left[\begin{array}{c}2\\-3\end{array}\right]\\\\\left[\begin{array}{cc}3&2\\5&5\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}1\\-5\end{array}\right]\\\\\left[\begin{array}{c}x\\y\end{array}\right]=(1)/(5)\left[\begin{array}{cc}5&-2\\-5&3\end{array}\right]\left[\begin{array}{c}1\\-5\end{array}\right]`

Performing the multiplication of the matrix by the vector gives the solution.

x = ((5)(1) +(-2)(-5))/5 = 15/5 = 3

y = ((-5)(1) +(3)(-5))/5 = -20/5 = -4

Using your variables, x1, x2, the solution is ...

(x1, x2) = (3, -4)