solve using cramer's rule
3x+4y=-1
5x-2y=4
First calculate the determinant D of
3 4
5 -2
=3*(-2)-4*5=-26
Replace the first column by the RHS,and calculate determinant D1
-1 4
4 -2
=(-1)(-2)-4*4
=-14
Replace the column with the RHS and calculate determinant D2
3 -1
5 4
=3*4-(-1)*5
=17
x=D1/D=-14/-26=7/13
y=D2/D=17/-26=-17/26
To solve the system of equations using Cramer's rule, we need to find the values of x and y by applying Cramer's rule.
Cramer's rule states that if we have a system of linear equations in the form Ax + By = C and Dx + Ey = F, the solution can be found using the following formulas:
x = (C * Ey - B * F) / (A * E - B * D)
y = (A * F - C * D) / (A * E - B * D)
Let's apply Cramer's rule to the given system of equations:
Equation 1: 3x + 4y = -1 (denoted by A, B, and C)
Equation 2: 5x - 2y = 4 (denoted by D, E, and F)
First, let's calculate the determinants of the coefficients:
Determinant D =
| A B |
| D E |
D = (3 * -2) - (4 * 5) = -6 - 20 = -26
Determinant Dx =
| C B |
| F E |
Dx = (-1 * -2) - (4 * 4) = 2 - 16 = -14
Determinant Dy =
| A C |
| D F |
Dy = (3 * 4) - (-1 * 5) = 12 + 5 = 17
Now, let's find the values of x and y using the formulas:
x = Dx / D = -14 / -26 = 7/13
y = Dy / D = 17 / -26 = -17/26
Therefore, the solution to the system of equations using Cramer's rule is x = 7/13 and y = -17/26.