Question

Solve the following simultaneous equations using an algebraic method:

1) 4x + 3y = 7
2) 3x - 2y = 18.

Answer 1

To solve the given simultaneous equations, we use the substitution method to find x = 4 and y = -3 as the solution to the system.

Step-by-step explanation:

To solve the simultaneous equations for the unknowns x and y, we will use the substitution or elimination method. Given the equations:

1. 4x + 3y = 7 (1)
2. 3x - 2y = 18 (2)

We can solve one of the equations for one variable and substitute it into the other. Let's solve the first equation for y:

3y = 7 - 4x

y = (7 - 4x) / 3 (3)

Now we can substitute equation (3) into equation (2):

3x - 2((7 - 4x) / 3) = 18

Multiplying through by 3 to clear fractions gives:

9x - 2(7 - 4x) = 54

Distributing the -2:

9x - 14 + 8x = 54

Combining like terms:

17x = 68

Dividing by 17:

x = 4

Substitute x = 4 into equation (3) to find y:

y = (7 - 4*4) / 3

y = (7 - 16) / 3

y = -9 / 3

y = -3

Thus, the solution to the system of equations is x = 4 and y = -3.