4x−6y=−48
−2x+4y=30
To solve this system of equations, we can use the method of substitution.
First, let's solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:
-2x + 4y = 30
-2x = -4y + 30
x = 2y - 15
Now, let's substitute this value of x into the first equation:
4(2y - 15) - 6y = -48
8y - 60 - 6y = -48
2y - 60 = -48
2y = -48 + 60
2y = 12
y = 12/2
y = 6
Now that we have the value of y, we can substitute it back into either equation to find x. Let's substitute it into the second equation:
-2x + 4(6) = 30
-2x + 24 = 30
-2x = 30 - 24
-2x = 6
x = 6/(-2)
x = -3
Therefore, the solution to the system of equations is x = -3 and y = 6.
To solve the system of equations:
4x - 6y = -48 ........(1)
-2x + 4y = 30 .......(2)
Step 1: Let's eliminate one variable by multiplying equation (2) by 2 to make the coefficient of "x" the same but with opposite signs as in equation (1).
2(-2x + 4y) = 2(30)
-4x + 8y = 60 .......(3)
Step 2: Now, we will add equation (1) and equation (3) to eliminate "x".
(4x - 6y) + (-4x + 8y) = -48 + 60
-6y + 8y = 12
2y = 12
Step 3: Divide both sides of the equation by 2 to solve for "y".
2y / 2 = 12 / 2
y = 6
Step 4: Substitute the value of "y" into one of the original equations (either equation (1) or equation (2)) to solve for "x". Let's use equation (1).
4x - 6(6) = -48
4x - 36 = -48
Step 5: Add 36 to both sides of the equation.
4x - 36 + 36 = -48 + 36
4x = -12
Step 6: Divide both sides of the equation by 4 to solve for "x".
4x / 4 = -12 / 4
x = -3
So, the solution to the system of equations is x = -3 and y = 6.
To solve the system of equations:
4x - 6y = -48 ...(Equation 1)
-2x + 4y = 30 ...(Equation 2)
There are a few different methods you can use to solve a system of equations, such as substitution, elimination, or graphing. Let's use the method of substitution to find the solution.
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve Equation 2 for x:
-2x + 4y = 30
-2x = -4y + 30
Divide both sides by -2:
x = 2y - 15 ...(Equation 3)
Step 2: Substitute the expression for x from Equation 3 into Equation 1:
4x - 6y = -48
4(2y - 15) - 6y = -48
Distribute 4:
8y - 60 - 6y = -48
Combine like terms:
2y - 60 = -48
Add 60 to both sides:
2y = 12
Divide by 2:
y = 6
Step 3: Substitute the value of y into Equation 3 to find x:
x = 2(6) - 15
x = 12 - 15
x = -3
Therefore, the solution to the system of equations is x = -3 and y = 6.