2.
x = -1 , y = 4
3.
x = 7, y = -1
4.
x = 1, y = 2
Step-by-step explanation:
2. 6x + 2y = 2, -3x - 4y = -13
3. 4x + 8y = 20, -4x + 2y = -30
4. y = -3x + 5, 5x - 4y = -3
2.
We have to determine the solutions of this system of equations, basically look for x and y. First, let's solve through elimination.
6x + 2y = 2
-3x - 4y = -13
Multiply the second equation by 2 :
6x + 2y = 2
-6x - 8y = -26
Add the equations and solve for y :
-6y = -24
Divide both sides by -6 :
y = 4
Now that we have found y, we can substitute 4 in y of the first equation :
6x + 2(4) = 2
6x + 8 = 2
Subtract 8 from both sides :
6x = -6
Divide both sides by 6 :
x = -1
3.
4x + 8y = 20
-4x + 2y = -30
We are asked to solve in elimination style, do as followed :
4x + 8y = 20
-4x + 2y = -30
Add and solve for y :
10y = -10
Divide 10 from both sides to get y alone :
y = -1
Now that we know y, we can substitute it into the first equation :
4x + 8(-1) = 20
4x - 8 = 20
Add 8 to both sides :
4x = 28
Divide 4 from both sides :
x = 7
4.
y = -3x + 5
5x - 4y = -3
We are asked to solve with substitution :
Since the first equation has y alone, we can replace it with y in the second equation :
5x - 4(-3x + 5) = -3
Distribute :
5x + 12x - 20 = -3
Combine like terms :
17x - 20 = -3
Add 20 to both sides :
17x = 17
Divide 17 from both sides :
x = 1
Now that we know y, we can substitute x in the first equation with 1 :
y = -3(1) + 5
y = -3 + 5
y = 2
