Solve the system of two equations using elimination with multiplication.
4х - 6y = -48
-2x + 4y = 30 (1 point)
A. (-3, 6)
B. (21, -6)
C. (3, 9)
D. (-33, -9)
To solve the system of equations using elimination with multiplication, we need to eliminate one variable by multiplying one or both of the equations by a constant that will create opposite coefficients for that variable.
In this case, we can see that if we multiply the first equation by 2, and the second equation by 3, the coefficients of x in both equations will become -12 and 6 respectively, which will allow us to eliminate x.
Multiplying the first equation by 2:
8x - 12y = -96
Multiplying the second equation by 3:
-6x + 12y = 90
Now, we can add the two equations together to eliminate y:
(8x - 12y) + (-6x + 12y) = -96 + 90
2x = -6
x = -3
Now that we have the value of x, we can substitute it back into either of the original equations to solve for y. 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 (-3, 6), which corresponds to option A. (-3, 6)
How many solutions does the system of equations have?
8х - 6y = 48
8x + 6y = 48
A. one
B. infinite
C. none
D. two
To determine the number of solutions the system of equations has, we can simplify the equations and compare them.
If we add the two equations together, we get:
(8x - 6y) + (8x + 6y) = 48 + 48
16x = 96
x = 96/16
x = 6
Now, we substitute the value of x back into one of the original equations, let's use the first one:
8(6) - 6y = 48
48 - 6y = 48
-6y = 48 - 48
-6y = 0
y = 0
We see that the value of y is 0.
Therefore, the system of equations has one solution: (6, 0). The answer is option A. one.
To solve the system of equations using elimination with multiplication, we need to eliminate one variable by multiplying one or both equations. Let's start by multiplying the second equation by 2:
2 * (-2x + 4y) = 2 * 30
-4x + 8y = 60
Now the system of equations becomes:
4x - 6y = -48
-4x + 8y = 60
Adding the two equations together will eliminate the x variable:
(4x - 6y) + (-4x + 8y) = -48 + 60
-6y + 8y = 12
2y = 12
y = 12/2
y = 6
Now we can substitute the value of y back into one of the original equations, let's use the first equation:
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). So the answer is A. (-3, 6).
To solve the system of equations using elimination with multiplication, we need to eliminate one variable by multiplying the equations so that the coefficients of one variable are the same, but with opposite signs.
Step 1: Multiply one or both of the equations by some numbers so that the coefficients of one variable are the same (but with opposite signs). In this case, we can multiply the first equation by 2 and the second equation by 3 to achieve this:
Equation 1: 8x - 12y = -96
Equation 2: -6x + 12y = 90
Step 2: Now, add the two equations together to eliminate the y variable:
(8x - 12y) + (-6x + 12y) = -96 + 90
Simplifying the equation gives:
8x - 12y - 6x + 12y = -6
(8x - 6x) + (-12y + 12y) = -6
2x + 0 = -6
2x = -6
Step 3: Solve for x by dividing both sides of the equation by 2:
2x/2 = -6/2
x = -3
Step 4: Substitute the value of x (-3) into either of the original equations to solve for y:
Using the first equation:
4x - 6y = -48
4(-3) - 6y = -48
-12 - 6y = -48
-6y = -48 + 12
-6y = -36
Step 5: Solve for y by dividing both sides of the equation by -6:
-6y/-6 = -36/-6
y = 6
Therefore, the solution to the system of equations is x = -3 and y = 6, which corresponds to point (-3, 6).
So the correct answer is A. (-3, 6).