What is the value of the expression 5x - 3y ?
3x - 4y= -24
3x +2y= -6
We can use a system of equations to solve for the values of x and y, and then substitute those values into the expression 5x - 3y.
First, we can use the method of elimination to eliminate x from the two equations:
(3x - 4y) - (3x + 2y) = -24 - (-6)
-6y = -18
y = 3
Substituting y = 3 into one of the original equations to solve for x:
3x + 2(3) = -6
3x + 6 = -6
3x = -12
x = -4
Now that we have found the values of x and y, we can substitute them into the expression 5x - 3y:
5(-4) - 3(3) = -20 - 9 = -29
Therefore, the value of the expression 5x - 3y is -29.
To find the value of the expression 5x - 3y, we need to solve the system of equations first. Let's solve the system of equations using the method of elimination:
Given equations:
1) 3x - 4y = -24
2) 3x + 2y = -6
Multiplying equation 1) by 2 and equation 2) by -4 to eliminate x:
3) 6x - 8y = -48
4) -12x - 8y = 24
Adding equations 3) and 4) to eliminate y:
6) -6x = -24
Dividing both sides of equation 6) by -6:
x = 4
Substituting the value of x into equation 1) or 2) to find y. Let's use equation 1):
3(4) - 4y = -24
12 - 4y = -24
Rearranging the equation:
-4y = -24 - 12
-4y = -36
Dividing both sides of the equation by -4:
y = 9
Now, substitute the values of x = 4 and y = 9 into the expression 5x - 3y:
5(4) - 3(9) = 20 - 27 = -7
Therefore, the value of the expression 5x - 3y is -7.
To find the value of the expression 5x - 3y, we need to first find the values of x and y that satisfy the given system of equations:
1. Start by solving the system of equations using the method of substitution or elimination.
Let's solve using the method of elimination:
Multiply the second equation by 2 to eliminate the x term:
2(3x + 2y) = 2(-6)
6x + 4y = -12
2. Subtract the first equation from the equation obtained in step 1 to eliminate the y term:
(6x + 4y) - (3x - 4y) = -12 - (-24)
6x + 4y - 3x + 4y = 12 + 24
3x + 8y = 36
3. Now we have a new equation: 3x + 8y = 36
4. Solve the new equation for x or y. Let's solve it for x:
3x + 8y = 36
3x = 36 - 8y
x = (36 - 8y) / 3
5. Substitute the value of x into any of the original equations. Let's use the first equation:
3x - 4y = -24
3 * ((36 - 8y) / 3) - 4y = -24
36 - 8y - 4y = -24
36 - 12y = -24
-12y = -24 - 36
-12y = -60
y = (-60) / (-12)
y = 5
6. Substitute the value of y into the value of x we found earlier:
x = (36 - 8y) / 3
x = (36 - 8(5)) / 3
x = (36 - 40) / 3
x = (-4) / 3
Therefore, the value of the expression 5x - 3y is:
5(-4/3) - 3(5)
-20/3 - 15
-20/3 - 45/3
(-20 - 45) / 3
-65/3
So, the value of the expression 5x - 3y is -65/3.