3x+6y=21 -5x+2y=13
To solve this system of equations, we can use either the substitution method or the elimination method.
Let's use the elimination method:
1) First, let's multiply the second equation by 3 to make the coefficients of x in both equations equal:
-15x + 6y = 39
2) Now, we can add the two equations together to eliminate x:
3x + 6y = 21
-15x + 6y = 39
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-12x = 60
3) Now, divide by -12 to solve for x:
x = -5
4) Now, substitute the value of x back into either of the original equations to solve for y. Let's use the first equation:
3(-5) + 6y = 21
-15 + 6y = 21
6y = 36
y = 6
Therefore, the solution to the system of equations is x = -5 and y = 6.
wrong
Let's try solving the system of equations again using the substitution method:
From equation 1:
3x + 6y = 21
6y = 21 - 3x
y = (21 - 3x) / 6
y = (7 - x) / 2
Now, substitute this expression for y in the second equation:
-5x + 2y = 13
-5x + 2((7 - x) / 2) = 13
-5x + 7 - x = 13
-6x + 7 = 13
-6x = 6
x = -1
Substitute x = -1 back into the expression for y:
y = (21 - 3(-1)) / 6
y = (21 + 3) / 6
y = 24 / 6
y = 4
Therefore, the solution to the system of equations is x = -1 and y = 4.