Question

Solve these simultaneous equations using the elimination method:

a−2b=−5
3a+4b=0

a) a=−2,b=1
b) a=1,b=−2
c) a=−1,b=2
d) a=2,b=−1

Answer 1

To solve the simultaneous equations using the elimination method, we first eliminate one variable by adding or subtracting the equations. Then, we solve for the remaining variable. In this case, the solution is a = -2.2222 and b = 1.5.

Step-by-step explanation:

To solve the simultaneous equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations. Let's start by multiplying the first equation by 3 and the second equation by 2 to make the coefficients of 'a' opposite. This gives us:

3a - 6b = -15

6a + 8b = 0

Next, we can add the two equations together:

9a + 2b = -15

6a + 8b = 0

Multiplying the first equation by 4 and the second equation by -3 gives us:

36a + 8b = -60

-18a - 24b = 0

Adding these two equations together, we get:

18a - 16b = -60

So, the simplified system of equations is:

9a + 2b = -15

18a - 16b = -60

To eliminate 'b', we can multiply the first equation by 8 and the second equation by 2:

72a + 16b = -120

36a - 32b = -120

Adding these equations together, we get:

108a = -240

Dividing both sides by 108, we find that 'a' equals -240/108 or approximately -2.2222.

Substituting this value of 'a' back into the first equation, we can solve for 'b':

-18 + 2b = -15

2b = 3

b = 3/2 or 1.5

Therefore, the solution to the system of equations is:

a = -2.2222, b = 1.5