Solve the system of two equations using elimination with multiplication.
4x−6y=−48
−2x+4y=30 (1 point)
Responses
(−3, 6)
left parenthesis negative 3 comma 6 right parenthesis
(−33,−9)
left parenthesis negative 33 comma negative 9 right parenthesis
(3, 9)
left parenthesis 3 comma 9 right parenthesis
(−21,−6)
To solve the system of equations using elimination with multiplication, we want to eliminate one variable by multiplying both equations by appropriate numbers.
First, let's multiply the second equation by 2 to eliminate the coefficient of "-2x":
2(-2x + 4y) = 2(30)
-4x + 8y = 60
Now, we have the following system of equations:
4x - 6y = -48
-4x + 8y = 60
By adding the two equations together, we can eliminate the "x" variable:
(4x - 6y) + (-4x + 8y) = -48 + 60
-6y + 8y = 12
2y = 12
y = 6
Substitute the value of "y" back into one of the original equations:
4x - 6(6) = -48
4x - 36 = -48
4x = -48 + 36
4x = -12
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 manipulate the equations by multiplying them by a suitable factor so that the coefficients of one of the variables become the same, but with opposite signs.
Let's start by multiplying the first equation by 2 and the second equation by 3 to make the coefficient of x the same:
2(4x - 6y) = 2(-48) becomes 8x - 12y = -96
3(-2x + 4y) = 3(30) becomes -6x + 12y = 90
Now we can add the two equations together to eliminate the y variable:
(8x - 12y) + (-6x + 12y) = -96 + 90
8x - 6x - 12y + 12y = -6
Simplifying further:
2x = -6
x = -3
Now we substitute the value of x into one of the original equations, let's use the first equation:
4(-3) - 6y = -48
-12 - 6y = -48
-6y = -48 + 12
-6y = -36
y = -36 / -6
y = 6
Therefore, the solution to the system of equations is (x, y) = (-3, 6).
To solve the system of equations using elimination with multiplication, we will eliminate one of the variables by multiplying one or both equations by a constant. Let's start with the given equations:
1) 4x - 6y = -48
2) -2x + 4y = 30
The goal is to eliminate one of the variables by making the coefficients of either x or y the same in both equations. Let's focus on eliminating the x term.
We can multiply Equation 1) by 2 to make the coefficient of x equal to -4, which will cancel out the x term.
2 * (4x - 6y) = 2 * (-48)
8x - 12y = -96
Now, we have two equations:
3) 8x - 12y = -96
4) -2x + 4y = 30
Next, add Equation 3) and Equation 4) together to eliminate the x term.
(8x - 12y) + (-2x + 4y) = -96 + 30
6x - 8y = -66
Now we have a new equation:
5) 6x - 8y = -66
We can simplify this equation by dividing each term by 2:
(6x/2) - (8y/2) = -66/2
3x - 4y = -33
Now, we have a new equation:
6) 3x - 4y = -33
Now, we have eliminated the x term. To solve for y, we can multiply Equation 6) by -3 and add it to Equation 5) to eliminate the y term.
-3 * (3x - 4y) = -3 * (-33)
-9x + 12y = 99
Now, we have two equations:
7) -9x + 12y = 99
8) 6x - 8y = -66
Add Equation 7) and Equation 8) together:
(-9x + 12y) + (6x - 8y) = 99 + (-66)
-3x + 4y = 33
Now, we have a new equation:
9) -3x + 4y = 33
We can simplify this equation by dividing each term by -1:
(-3x/-1) + (4y/-1) = 33/-1
3x - 4y = -33
Now, we have the same equation as Equation 6).
Equation 9) is equivalent to Equation 6) as both represent the same line. This means that the system of equations is dependent and has infinitely many solutions.
Thus, there is not a unique solution for the system of equations using elimination with multiplication.