use elimination to solve this problem
x +8y = 3
4x - 2y = 7
first one times 4 ----> 4x + 32y = 12
keep the the 2nd ----> 4x - 2y = 7
subtract them
34y = 5
y = 5/34
sub into original first
x + 8(5/34) = 3
x = 3 - 40/34 = 31/17
x = 31/17 , y = 5/34
( checked the answer)
To solve this system of equations using elimination, we need to eliminate one variable by adding or subtracting the two equations. Let's start by multiplying the first equation by 2:
2(x + 8y) = 2(3)
2x + 16y = 6
Now we have:
2x + 16y = 6
4x - 2y = 7
Now, notice that if we add these two equations together, the x variable will be eliminated. Let's do that:
(2x + 16y) + (4x - 2y) = 6 + 7
6x + 14y = 13
Now we have a new equation:
6x + 14y = 13
To eliminate the y variable, we multipy the first equation by -7:
-7(x + 8y) = -7(3)
-7x - 56y = -21
Now we have:
-7x - 56y = -21
6x + 14y = 13
If we add these two equations together, the y variable will be eliminated:
(-7x - 56y) + (6x + 14y) = -21 + 13
-x - 42y = -8
Now we have another new equation:
-x - 42y = -8
Now, we have two equations left:
6x + 14y = 13
-x - 42y = -8
We can solve this system of equations by using any method, such as substitution or graphing.