solve the systems of equation: First : 4x-2y = 2 Second: y = -4x-7
Should i solve by using substitution, elimination or multiply then use elimination?
Try adding them. Add up the left sides and the right sides (after rearranging the second equation) the x term will drop out, giving you
4x -2y = 2
-4x-y = 7
-3y = 9
y = -3
For x, substitute y=-3 into the first equation
x = (1/4)(2 +2y) = -1
/2
To solve the system of equations:
First: 4x - 2y = 2
Second: y = -4x - 7
You can use the method of elimination. Rearrange the second equation to match the format of the first equation:
Second: 4x + y = -7
Now, add the two equations together to eliminate the x term:
(4x - 2y) + (4x + y) = 2 + (-7)
8x - y = -5
Now, you have a new equation:
8x - y = -5
Next, solve for y by rearranging the equation:
-y = -5 - 8x
y = 8x + 5
Now that you have the value of y, substitute it back into one of the original equations to solve for x. Let's substitute it into the second equation:
8x + 5 = -4x - 7
Combine like terms:
8x + 4x = -7 - 5
12x = -12
Divide both sides by 12:
x = -1
Now that you know x = -1, substitute it back into one of the original equations to solve for y. Let's substitute it into the first equation:
4(-1) - 2y = 2
Simplify:
-4 - 2y = 2
Add 4 to both sides:
-2y = 6
Divide both sides by -2:
y = -3
So, the solution to the system of equations is x = -1 and y = -3.
To solve the system of equations using the elimination method, you would need to multiply one of the equations by a certain factor so that when you add or subtract the two equations, one of the variables will be eliminated.
In this case, there's no need to multiply either equation because the coefficients of the x term in both equations are already opposites. This means you can simply add the two equations together to eliminate the x term.
Let's add the equations:
4x - 2y = 2
+ (-4x - y = 7)
-------------------
0x - 3y = 9
Simplifying further, we get:
-3y = 9
Now, we solve for y by dividing both sides by -3:
y = -3
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
4x - 2y = 2
4x - 2(-3) = 2
4x + 6 = 2
4x = 2 - 6
4x = -4
x = -4/4
x = -1
Thus, the solution to the system of equations is x = -1 and y = -3.