Exercise 40 Page 210

We will use Cramer's Rule to solve the given system of equations and find the intersection point of the two given lines. 3x - 1y= 5x+2y=22 Let C be the coefficient matrix of the system. The coefficient matrix is a matrix that contains only the coefficients of the system. C= [ cc 3 & -1 5 & 2 ] If the determinant of the coefficient matrix, |C|, is different from zero, we can find the solution to our system, (x,y), by using determinants. x=| cc & -1 22 & 2 |/|C| and y= | cc 3 & 5 & 22 |/|C| Let's start by calculating |C|.

We can now substitute 11 for |C| and calculate the value of x.

Finally, we will substitute 11 for |C| in the formula for y.

The solution of the system, which is the point of intersection of the lines, is (2,6).