Solve the system of equations. 3x−4y=40 5x−5y=55 (1 point) Responses (4,−7) left parenthesis 4 comma negative 7 right parenthesis (14, 3) left parenthesis 14 comma 3 right parenthesis (18, 7) left parenthesis 18 comma 7 right parenthesis (8,−3)
Let's solve the system of equations using the method of substitution:
From the first equation, we can solve for x in terms of y:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3
Now we substitute this expression for x into the second equation:
5x - 5y = 55
5((4y + 40)/3) - 5y = 55
(20y + 200)/3 - 5y = 55
(20y + 200) - 15y = 165
20y - 15y + 200 = 165
5y + 200 = 165
5y = -35
y = -7
Now substitute this value of y back into the expression for x:
x = (4(-7) + 40)/3
x = ((-28) + 40)/3
x = 12/3
x = 4
Therefore, the solution to the system of equations is (x, y) = (4, -7).
To solve the system of equations:
1) Start by multiplying both sides of the second equation by 4 to make the coefficients of x in both equations the same.
5x - 5y = 55 becomes 20x - 20y = 220.
2) Now, we have two equations:
3x - 4y = 40
20x - 20y = 220.
3) Multiply the first equation by 5 to make the coefficients of x in both equations the same.
5*(3x - 4y) = 5*40.
Simplify: 15x - 20y = 200.
4) Now, we have two equations:
15x - 20y = 200
20x - 20y = 220.
5) Subtract the second equation from the first equation to eliminate the y variable.
(15x - 20y) - (20x - 20y) = 200 - 220.
Simplify: -5x = -20.
Divide both sides of the equation by -5 to solve for x:
x = -20 / -5.
Simplify: x = 4.
6) Substitute the value of x into either equation. Let's use the first equation:
3x - 4y = 40
3*4 - 4y = 40.
Simplify: 12 - 4y = 40.
Subtract 12 from both sides of the equation:
-4y = 40 - 12.
Simplify: -4y = 28.
Divide both sides of the equation by -4 to solve for y:
y = 28 / -4.
Simplify: y = -7.
Therefore, the solution to the system of equations is (4, -7).
To solve the system of equations, you can use the method of substitution or elimination. Let's use the method of elimination.
1. Start with the given system of equations:
3x - 4y = 40 ...(Equation 1)
5x - 5y = 55 ...(Equation 2)
2. Multiply Equation 1 by 5 and Equation 2 by 3 to make the coefficients of the x terms equal:
15x - 20y = 200 ...(Equation 3)
15x - 15y = 165 ...(Equation 4)
3. Now, subtract Equation 4 from Equation 3 to eliminate the x term:
(15x - 20y) - (15x - 15y) = 200 - 165
-20y + 15y = 35
-5y = 35
4. Solve for y:
Divide both sides of the equation by -5:
-5y / -5 = 35 / -5
y = -7
5. Substitute the value of y = -7 back into any of the original equations to find x. Let's use Equation 1:
3x - 4(-7) = 40
3x + 28 = 40
3x = 40 - 28
3x = 12
6. Solve for x:
Divide both sides of the equation by 3:
3x / 3 = 12 / 3
x = 4
7. Therefore, the solution to the system of equations is (x, y) = (4, -7).
So the correct response is:
(4, -7)