The problem using elimination/substitution methods what is the solution set to 3x -2y =-4 and 5x=2y the choices
a)(2,-5)
b)(-2,-5)
c)(2,5)
d)(-2,5)
Please, Please, Please, HELP!
Between a and c I believe it is c is that correct?
Yes.
To solve the system of equations using elimination/substitution method, we can proceed as follows:
1. Elimination Method:
Start by multiplying the second equation, 5x = 2y, by 2 to make the coefficients of y in both equations the same. This gives us:
10x = 4y
Now, we can subtract the first equation, 3x - 2y = -4, from this new equation:
10x - (3x - 2y) = 4y - (-4)
10x - 3x + 2y = 4y + 4
7x + 2y = 4y + 4
2. Substitution Method:
Solve the second equation, 5x = 2y, for either x or y. Let's solve it for x:
x = (2/5)y
Now substitute this value of x into the first equation, 3x - 2y = -4:
3((2/5)y) - 2y = -4
(6/5)y - (10/5)y = -4
(6/5 - 10/5)y = -4
(-4/5)y = -4
Divide both sides of the equation by (-4/5) to solve for y:
y = -4 / (-4/5)
y = -4 * (-5/4)
y = 5
Now substitute the value of y = 5 back into the second equation, 5x = 2y:
5x = 2(5)
5x = 10
x = 10/5
x = 2
So, the solution to the system of equations 3x - 2y = -4 and 5x = 2y is x = 2 and y = 5.
Now, let's check the answer options:
a) (2, -5)
When x = 2, y = -5
Substituting these values into the equations:
3(2) - 2(-5) = -4
6 + 10 = -4 (which is false)
c) (2, 5)
When x = 2, y = 5
Substituting these values into the equations:
3(2) - 2(5) = -4
6 - 10 = -4 (which is true)
Therefore, the correct solution set is c) (2, 5).