How do you solve this by linear combinations?
4x+3y=-8
3x-3y=15
L1 : 4x+3y=-8
L2 : 3x-3y=15
Do L1+L2--> 7x=7 so x=1
in L1 4*(1)+3y=-8
3y=-12
y=-4
the couple of solution is(1,-4)
How did you get x=1? by pugging it in with the 8 right?
No. Add equation 1 (what mk-tintin labels L1) to equation 2, (L2) to obtain
7x +0y = -8+15
7x=7
x=1
doing L1+L2-->4x+3x+3y-3y=-8+15
--->7x=7
x=1
do u understand?
Oh i was looking at it all wrong alright i understand it a bit better now, doh was plugging in the wrong numbers haha. Sorry.
To solve this system of equations using the method of linear combinations, you need to eliminate one variable by adding or subtracting the equations. Let's walk through the steps to solve it:
Step 1: Multiply the second equation by 4 to make the y-coefficients opposite and equal to eliminate the y-variable. This gives us:
4(3x - 3y) = 4(15)
12x - 12y = 60
The new system of equations becomes:
1) 4x + 3y = -8
2) 12x - 12y = 60
Now, we can combine these two equations to eliminate y.
Step 2: Add equation 1) and equation 2) together.
(4x + 3y) + (12x - 12y) = -8 + 60
16x - 9y = 52
Now we have a new equation with only one variable, x. Let's continue to solve for x.
Step 3: Solve the resulting equation for x.
16x - 9y = 52
16x = 52 + 9y
x = (52 + 9y) / 16
Step 4: Substitute the value of x in terms of y back into one of the original equations to find y. Let's substitute x in equation 1):
4x + 3y = -8
4((52 + 9y) / 16) + 3y = -8
(52 + 9y)/4 + 3y = -8
Solve for y:
52 + 9y + 12y = -32
21y = -84
y = -84 / 21
y = -4
Step 5: Substitute the value of y back into the equation for x to find x:
x = (52 + 9y) / 16
x = (52 + 9(-4)) / 16
x = (52 - 36) / 16
x = 16 / 16
x = 1
Therefore, the solution to the system of equations is x = 1 and y = -4.