Solve using elimination

2x+5y=-23
5x+13y=-60

x = 1

y = -5

Step-by-step explanation:

This is a simultaneous equation question.

We are given two equations and we shall label the equations as equation 1 and 2.

2x + 5y = -23 (i)

5x + 13y = -60(ii)

Step one

First step to solving simultaneous equations by elimination method is to ensure one of the terms that has an unknown, (in this case, either x or y) is the equal in the two equations.

To do this, we multiply equation one by 5 and equation two by 2

5 x (i) = 10x + 25y = -115 (iii)

2 x (ii) = 10x + 26y = -120(iv)

To eliminate the term that has x, we subtract equation (iii) from equation (iv)

(iv) - (iii) =

(10x - 10x) + (26y - 25y) = -120 - (-115)

y = -5

We substitute the new value of y = -5 into equation (i)

2x + 5y = -23

2x + 5(-5) = -23

2x - 25 = -23

We collect like terms by adding 25 to both sides of the equation

2x - 25 + 25 = -23 + 25

2x = 2

We divide both sides of the equation by the coefficient of x to find the value of x. The coefficient of x is 2

2x/2 = 2/2

x = 1

Therefore, the solutions to the simultaneous equations using elimination method are

x = 1 and y = -5

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