Solve the system of equations.
−4x+6y=38
x−5y=−20 (1 point)
Responses
(35, −3)
left parenthesis 35 comma negative 3 right parenthesis
(5, 3)
left parenthesis 5 comma 3 right parenthesis
(−5, 3)
left parenthesis negative 5 comma 3 right parenthesis
(−35, −3)
To solve the system of equations −4x+6y=38 and x−5y=−20, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one of the equations for one variable.
We'll solve the second equation, x−5y=−20, for x:
x = 5y - 20
Step 2: Substitute the expression for x in the other equation.
We substitute 5y - 20 for x in the first equation:
−4(5y - 20) + 6y = 38
Simplify and solve for y:
-20y + 80 + 6y = 38
-20y + 6y = 38 - 80
-14y = -42
y = -42 / -14
y = 3
Step 3: Substitute the value of y back into one of the original equations to solve for x.
Let's substitute y = 3 into x−5y=−20:
x - 5(3) = -20
x - 15 = -20
x = -20 + 15
x = -5
Therefore, the solution to the system of equations is (−5, 3).
To solve the system of equations, we can use the method of substitution or elimination.
Let's use the elimination method.
We have the equations:
1) -4x + 6y = 38
2) x - 5y = -20
To eliminate x, we can multiply equation 2) by 4 to make the coefficients of x in both equations equal.
Multiplying equation 2) by 4, we get:
4(x - 5y) = 4(-20)
4x - 20y = -80
Now we can subtract equation 1) from this new equation to eliminate x:
(4x - 20y) - (-4x + 6y) = -80 - 38
4x - 20y + 4x - 6y = -118
8x - 26y = -118
Now we have a new equation:
3) 8x - 26y = -118
Combining equations 1) and 3), we have a system of equations with just one variable:
-4x + 6y = 38
8x - 26y = -118
Now we can solve for y in terms of x using equation 1):
-4x + 6y = 38
6y = 4x + 38
y = (4/6)x + 19/3
Substituting this value of y into equation 2):
x - 5(4/6)x - 5(19/3) = -20
x - (10/3)x - (95/3) = -20
(3/3)x - (10/3)x = (-20 + 95/3)
(-7/3)x = (-60 + 285/3)
To simplify this equation, we can multiply both sides by -3/7:
x = (-60 + 285/3)(-3/7)
x = (60/3 - 285/3)(3/7)
x = (60 - 285)/7
x = -225/7
Now we can substitute this value of x into the equation for y:
y = (4/6)(-225/7) + 19/3
y = -150/7 + 19/3
y = (-450 + 133)/21
y = -317/21
Therefore, the solution to the system of equations is (x, y) = (-225/7, -317/21), which can be rounded to approximately (x, y) ≈ (-32.14, -15.09).
Solve the system of equations. x%3D6y−3 2x%2B7y%3D13(1 point) (%2C )
To solve the system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution.
We have the equations:
1) x = 6y - 3
2) 2x + 7y = 13
We can substitute the value of x from equation 1) into equation 2):
2(6y - 3) + 7y = 13
12y - 6 + 7y = 13
19y - 6 = 13
19y = 19
y = 1
Now we can substitute the value of y = 1 into equation 1) to solve for x:
x = 6(1) - 3
x = 6 - 3
x = 3
Therefore, the solution to the system of equations is (x, y) = (3, 1).
Solve the system of equations. 8x−3y%3D −22 y%3D10%2B4x (1 point) (%2C )
To solve the system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution.
We have the equations:
1) 8x - 3y = -22
2) y = 10 + 4x
We can substitute the value of y from equation 2) into equation 1) to solve for x:
8x - 3(10 + 4x) = -22
8x - 30 - 12x = -22
-4x - 30 = -22
-4x = -22 + 30
-4x = 8
x = 8/(-4)
x = -2
Now we can substitute the value of x = -2 into equation 2) to solve for y:
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is (x, y) = (-2, 2).
Solve the system of equations. 5x%2B2y%3D14 x−6y%3D22(1 point) (%2C )
To solve the system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution.
We have the equations:
1) 5x + 2y = 14
2) x - 6y = 22
From equation 2), we can solve for x in terms of y:
x = 22 + 6y
Substituting this value of x into equation 1):
5(22 + 6y) + 2y = 14
110 + 30y + 2y = 14
110 + 32y = 14
32y = 14 - 110
32y = -96
y = -96/32
y = -3
Now we can substitute this value of y into equation 2) to solve for x:
x - 6(-3) = 22
x + 18 = 22
x = 22 - 18
x = 4
Therefore, the solution to the system of equations is (x, y) = (4, -3).
Solve the system of equations. –9x%2By%3D12 2x%2B4y%3D −28(1 point) (%2C )
To solve the system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution.
We have the equations:
1) -9x + y = 12
2) 2x + 4y = -28
From equation 1), we can solve for y in terms of x:
y = 9x + 12
Substituting this value of y into equation 2):
2x + 4(9x + 12) = -28
2x + 36x + 48 = -28
38x = -76
x = -76/38
x = -2
Now we can substitute this value of x into equation 1) to solve for y:
-9(-2) + y = 12
18 + y = 12
y = 12 - 18
y = -6
Therefore, the solution to the system of equations is (x, y) = (-2, -6).