Solve the system of two equations using elimination with multiplication. 4x−6y=−48 −2x+4y=30 (1 point) Responses (3, 9) left parenthesis 3 comma 9 right parenthesis (−3, 6) left parenthesis negative 3 comma 6 right parenthesis (−21,−6) left parenthesis negative 21 comma negative 6 right parenthesis (−33,−9)
First, we need to choose a coefficient to multiply one or both of the equations in order to eliminate one of the variables. In this case, it would be easiest to eliminate x.
Let's multiply the first equation by 2, and the second equation by 4:
8x - 12y = -96
-8x + 16y = 120
Now, add the two equations together:
(8x - 12y) + (-8x + 16y) = (-96) + 120
This simplifies to:
4y = 24
Divide both sides of the equation by 4:
y = 6
Now, substitute this value back into one of the original equations to solve for x. Let's use the first equation:
4x - 6(6) = -48
Simplify:
4x - 36 = -48
Add 36 to both sides of the equation:
4x = -12
Divide both sides of the equation by 4:
x = -3
Therefore, the solution to the system of equations is (-3, 6).
To solve the system of equations using elimination with multiplication, we can multiply one or both equations by a constant to make the coefficients of one of the variables the same but with opposite signs.
Let's multiply the second equation by 2 to make the coefficients of x opposites.
The original equations are:
4x - 6y = -48 ...(Equation 1)
-2x + 4y = 30 ...(Equation 2)
Multiplying Equation 2 by 2, we get:
-4x + 8y = 60
Now, we can add this equation to Equation 1 in order to eliminate x.
(4x - 6y) + (-4x + 8y) = -48 + 60
Simplifying:
-6y + 8y = 12
2y = 12
Dividing both sides of the equation by 2:
y = 6
Now, substitute the value of y back into either Equation 1 or Equation 2. Let's use Equation 1:
4x - 6(6) = -48
4x - 36 = -48
Add 36 to both sides:
4x = -48 + 36
4x = -12
Divide both sides of the equation by 4:
x = -12/4
x = -3
Therefore, the solution to the system of equations is (x, y) = (-3, 6).
To solve the system of equations using elimination with multiplication, we need to multiply one or both equations by a constant so that the coefficients of one of the variables will cancel out when the equations are added or subtracted.
Let's begin by multiplying the second equation by 2 to simplify the process:
Original equations:
4x - 6y = -48 ---- Equation (1)
-2x + 4y = 30 ---- Equation (2)
Multiplying Equation (2) by 2:
-4x + 8y = 60 ---- Equation (3)
Now, we need to add Equation (1) and Equation (3) together to eliminate the x-variable:
(4x - 6y) + (-4x + 8y) = (-48) + 60
Simplifying the equation, we can see that the x-variable cancels out:
-6y + 8y = 12
Combining like terms, we get:
2y = 12
Next, we divide both sides of the equation by 2 to solve for y:
2y/2 = 12/2
y = 6
Now, we substitute the value of y back into one of the original equations, such as Equation (1), and solve for x:
4x - 6(6) = -48
Simplifying the equation gives us:
4x - 36 = -48
Next, we add 36 to both sides of the equation:
4x - 36 + 36 = -48 + 36
Simplifying further, we have:
4x = -12
Finally, we divide both sides of the equation by 4 to solve for x:
4x/4 = -12/4
x = -3
Therefore, the solution to the system of equations is (x, y) = (-3, 6).