Solve using substitution.
y = x – 2
x + y = 10
7x + 2y = - 8
8y = 4x
Solve using elimination.
2x + 3y = 12
2x – y = 4
5x – 2y = - 19
2x + 3y = 0
5x-2y=0
Y=3+x
x + (x-2) = 10
2 x - 2 = 10
2 x = 12
x = 6
then y = (x-2) = 4
8 y = 4 x is x = 2 y
7(2y) + 2 y = -8
14 y + 2 y = 8
16 y = 8
y = 1/2
then x = 2y = 1
2 x + 3 y = 12
2 x - 1 y = 4
------------------subtract
0 x + 4 y = 8
y = 2
2 x - 2 = 4
x = 3
first line times 3, second times 2
15 x - 6 y = -57
+4 x + 6 y = 0
====================== add
19 x = -57
x = - 3
2(-3) + 3 y = 0
3 y = 6
y = 2
I show you one of them and the other one is your work ;) ..
(i) 7x + 2y = - 8
(ii) 8y = 4x
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i take equation (ii) and solve it for x:
8y=4x (divide by 4)
2y=x or x=2y (iii)
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now i take (i) and substitute (iii):
7(2y)+2y=-8
14y+2y=-8
16y=-8 (divide by 16
y=-0.5
____________
Now we get x from (iii):
x=2y=2*(-0.5)=-1
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(i) 2x + 3y = 12
(ii)2x – y = 4
----------------
(iii): 4y=8 ((i)-(ii))
(ii): 2x-y=4
----------------
(iii): y=2
insert in (ii): 2x-2=4 -> 2x=6 -> x=3
To solve the system of equations using substitution, follow these steps:
1. Start by isolating one variable in one equation. Let's isolate 'x' in the first equation:
y = x - 2
2. Substitute the expression for 'x' from the first equation into the second equation:
x + y = 10
x + (x - 2) = 10
3. Simplify the equation:
2x - 2 = 10
4. Solve for 'x':
2x = 12
x = 6
5. Now that we have the value of 'x', substitute it back into the first equation:
y = 6 - 2
y = 4
Therefore, the solution to the system of equations is x = 6 and y = 4.
To solve the system of equations using elimination, follow these steps:
1. Multiply both equations by appropriate coefficients to make the coefficients of 'y' equal:
Equation 1: 2x + 3y = 12 (unchanged)
Equation 2: 4x - 2y = 8
2. Add the equations together to eliminate the variable 'y':
(2x + 3y) + (4x - 2y) = 12 + 8
6x + y = 20
3. Solve for 'y':
y = 20 - 6x
4. Substitute the expression for 'y' back into either of the original equations. Let's use Equation 1:
2x - (20 - 6x) = 4
5. Simplify and solve for 'x':
2x - 20 + 6x = 4
8x - 20 = 4
8x = 24
x = 3
6. Substitute the value of 'x' back into Equation 1 to solve for 'y':
2(3) + 3y = 12
6 + 3y = 12
3y = 6
y = 2
Therefore, the solution to the system of equations is x = 3 and y = 2.