Question

What is the solution to this system of equations?
x = 12 − y
2x + 3y = 29

Answer 1

Let’s arrange the fist equation
x+y=12
2x+3y=29

Multiply equation 1 by 2
So it will be

2x+2y=24

Subtract eq 1 from eq 2

2x+3y=29
2x+2y=24
—————-
Y =5

Put value of y in eq 1

2x+2y=24
2x +10= 24
2x= 24-10
2x= 14
x=14/2
x=7

S.S= (7,5)

Answer 2

Explanation: I would use the substitution method for this system

because one of the variables, x, is already isolated in the first equation.

Since our first equation states that x = 12 - y, 12 - y can be substituted

in for x in the second equation which becomes 2(12 - y) + 3y = 29.

Now we can solve this equation by first distributing the 2

through the parentheses to get 24 - 2y + 3y = 29 and you

should be able to easily finish solving from here to get y = 5.

Now substitute a 5 back in for the first equation to get

x = 12 - (5) or x = 7 which means that our solution is (7, 5).