I have to use the substitution method to solve the system of equations.
4x-y=9 and 2x+3y=12
I worked this problem myself and could not find a possible solution. So I put that it is inconsistent. Is that correct? If not could you please help me?
from the 1st ---> 4x-9 = y
sub that into the 2nd
2x + 3(4x-9) = 12
2x + 12x - 27 = 12
14x = 39
x = 39/14
y = 4(39/14) - 9 = 15/7
check:
1st:
LS = 4(39/14) - 15/7
= 156/14 - 30/14
= 126/14 = 9 = RS
2nd:
LS = 2(39/14) + 3(15/7)
= 39/7+ 45/7
= 84/7 = 12 = RS
To solve the system of equations using the substitution method, you need to isolate one variable in terms of the other from one of the equations and then substitute that expression into the other equation.
Let's solve the system of equations step by step:
1. Start with the first equation:
4x - y = 9
2. Isolate either variable in terms of the other. Let's solve for y:
y = 4x - 9
3. Substitute this expression for y in the second equation:
2x + 3(4x - 9) = 12
4. Simplify and solve for x:
2x + 12x - 27 = 12
14x - 27 = 12
14x = 12 + 27
14x = 39
x = 39 / 14
x ≈ 2.786
5. Substitute the value of x back into either original equation to solve for y. Let's use the first equation:
4x - y = 9
4(2.786) - y = 9
11.144 - y = 9
-y = 9 - 11.144
-y = -2.144
y ≈ 2.144
Therefore, the solution to the system of equations is approximately x ≈ 2.786 and y ≈ 2.144.
Since you mentioned that you couldn't find a possible solution, it is possible that there was an error in your calculations. As shown above, there is a solution to this system of equations, so it is not inconsistent.