Use linear combinations to solve the system
3x − y = −4
−6x + y = 34
The value of x is
The value of y is
Just add them ....
-3x = 30
x = -10
back in the first
-30 - y = -4
-y = 26
y = -26
To solve the system of equations using linear combinations, we will eliminate one variable by adding or subtracting the equations.
First, let's eliminate y. Multiply the first equation by -1 and add the two equations together:
-(3x - y) = -(-4)
-3x + y = 4
-6x + y = 34
Adding these two equations, we get:
(-3x + y) + (-6x + y) = 4 + 34
-9x + 2y = 38
Since we have eliminated y, we can now solve for x:
-9x + 2y = 38
Rearrange this equation to isolate x:
-9x = 38 - 2y
Divide both sides by -9:
x = (38 - 2y) / -9
Now, let's substitute this value of x into one of the original equations to solve for y. Let's use the first equation:
3x - y = -4
Replace x with (38 - 2y) / -9:
3((38 - 2y) / -9) - y = -4
Multiply both sides by -9 to eliminate the fraction:
3(38 - 2y) - 9y = -4(-9)
114 - 6y - 9y = 36
Combine like terms:
-15y = 36 - 114
-15y = -78
Divide both sides by -15:
y = -78 / -15
y = 5.2
Finally, substitute the found value of y into either of the original equations to solve for x. Let's use the first equation:
3x - y = -4
Replace y with 5.2:
3x - 5.2 = -4
Add 5.2 to both sides:
3x = 5.2 - 4
3x = 1.2
Divide both sides by 3:
x = 1.2 / 3
x = 0.4
Therefore, the value of x is 0.4 and the value of y is 5.2.