4x-2y=7
3x+6y=9
Please help me solve this system by multiplying
12x-6y=21
3x+6y=9
now add them up and the y's are eliminated.
Should be easy going from there.
Thank you! So far, i have
12x-6y=21
3x+6y=9
--------
15x 30
---=--
15 15
Y = 2
Is this correct?
correct so far
You have only found the value of y, you still have to find x
sub y = 2 into either of the original equations to find x
To solve this system of equations by multiplying, we can use the method of elimination. Here's how you can do it step by step:
1. Multiply the entire first equation (4x - 2y = 7) by a factor that will make the coefficient of either x or y the same as the coefficient in the second equation (3x + 6y = 9). In this case, multiplying the first equation by 3 will give us:
3(4x - 2y) = 3(7)
12x - 6y = 21
2. Now compare the new equation (12x - 6y = 21) with the second equation (3x + 6y = 9). You can see that the coefficients of y (-6y and 6y) in both equations have opposite signs. To eliminate y, add the two equations together:
(12x - 6y) + (3x + 6y) = 21 + 9
15x = 30
3. Solve for x by dividing both sides of the equation by 15:
15x/15 = 30/15
x = 2
4. Substitute the value of x (which is 2) back into one of the original equations. Let's use the first equation (4x - 2y = 7):
4(2) - 2y = 7
8 - 2y = 7
5. Solve for y by isolating it on one side of the equation:
-2y = 7 - 8
-2y = -1
Divide both sides of the equation by -2 to find the value of y:
y = -1/-2
y = 1/2
So the solution to the system of equations is x = 2 and y = 1/2.