Solve the system of equations by using the Elimination method:
3x−2y+3=25
2x-7y-4=-12
To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the equations.
We'll start by eliminating the y variable. To do this, we'll need to multiply one or both of the equations by a constant so that the coefficients of y in both equations are the same.
To eliminate y, we can multiply the first equation by 7 and the second equation by 2.
7(3x - 2y + 3) = 7(25)
2(2x - 7y - 4) = 2(-12)
This gives us:
21x - 14y + 21 = 175
4x - 14y - 8 = -24
Now we have two equations with the same coefficient for y. We can subtract the second equation from the first equation to eliminate y.
(21x - 14y + 21) - (4x - 14y - 8) = 175 - (-24)
21x - 14y + 21 - 4x + 14y + 8 = 175 + 24
17x + 29 = 199
Next, we can isolate the x variable by subtracting 29 from both sides of the equation.
17x + 29 - 29 = 199 - 29
17x = 170
Now, divide both sides of the equation by 17 to solve for x.
17x/17 = 170/17
x = 10
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y.
Let's use the first equation:
3x - 2y + 3 = 25
Substituting x = 10:
3(10) - 2y + 3 = 25
30 - 2y + 3 = 25
-2y + 33 = 25
Next, we can isolate the y variable by subtracting 33 from both sides of the equation.
-2y + 33 - 33 = 25 - 33
-2y = -8
Now, divide both sides of the equation by -2 to solve for y.
-2y/-2 = -8/-2
y = 4
Therefore, the solution to the system of equations is x = 10 and y = 4.