Solve the system:4x+2y-13=0 and 3x=5y+26 by elimination.
3 (4x+2y-13=0)
12x+6y-26=0
4 (3x=5y+26)
12x=20y+104
I need to subtract since the signs are the same:
12x+6y-26=0
Since they don't match up, I'm having trouble subtracting them. I'm not sure what to do next. Please help??
3*(-13)=-39
so
12x+6y-39=0............(1)
change 4(3x=5y+26) to
4(3x-5y-26=0) =>
12x-20y-104=0 ...........(2)
(1)-(2)
26y+78=0
y=-3
Continue to solve for x, and check you answer by substitution.
To solve the system using elimination, you need to manipulate the equations in a way that allows you to eliminate one of the variables. In this case, one possible approach is to multiply the first equation by 3 and the second equation by 4, as you have correctly done.
However, there is a mistake in the calculations. When multiplying the first equation by 3, you should get:
3(4x + 2y - 13) = 0
12x + 6y - 39 = 0
And when multiplying the second equation by 4, you should get:
4(3x = 5y + 26)
12x = 20y + 104
Now, in order to eliminate the variable x, you need to make the coefficients of x in both equations equal. To do this, you can multiply the entire first equation by 3, which will make the coefficient of x equal to 12 in both equations:
3(12x + 6y - 39) = 0
36x + 18y - 117 = 0
Now you have the equations:
36x + 18y - 117 = 0
12x = 20y + 104
The next step is to subtract these equations to eliminate x. Since the coefficients of x in both equations are now equal, you can subtract equation 2 from equation 1:
(36x + 18y - 117) - (12x = 20y + 104) = 0
Simplifying this equation:
36x + 18y - 117 - 12x = 20y + 104
Combining like terms:
24x + 18y - 117 = 20y + 104
Now, you want to isolate one of the variables, either x or y. Let's isolate y by moving terms involving y to the right side:
24x - 20y + 18y = 117 + 104
Simplifying:
24x - 2y = 221
This is now a new equation that represents the system you started with. To solve for x and y, you would continue using methods such as substitution or elimination.