Given that: 4x – y + 9 = 0 and 3y – 2x = 7, solve for x.
does x=-2?
Yes. Could you not check your answer to see whether it fit the equations? That's faster than posting here and waiting for an answer.
from the first: y = 4x+9
sub into the 2nd:
3(4x+9) - 2x = 7
12x + 27 - 2x = 7
10x = -20
x = -2
you had that, but you only found x, you must also find y
sub x = -2 into y = 4x+9
y = -8+9 = 1
x = -2, y = 1
To solve for x in the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:
Given equations:
4x – y + 9 = 0 ...(1)
3y – 2x = 7 ...(2)
To eliminate the variable y, let's multiply equation (2) by 4:
12y - 8x = 28 ...(3)
Now, let's add equations (1) and (3) to eliminate the variable x:
(4x – y + 9) + (12y - 8x) = 0 + 28
Simplifying the equation:
4x - 8x - y + 12y + 9 = 28
Combining like terms:
-4x + 11y + 9 = 28
Now let's move the constants to the other side of the equation:
-4x + 11y = 28 - 9
-4x + 11y = 19 ...(4)
Now let's solve equation (4) for x:
-4x = 19 - 11y
Dividing both sides by -4:
x = (11y - 19) / 4
So, the value of x is (11y - 19) / 4. This means that x is not equal to -2 in general. The value of x depends on the value of y in the system of equations.