Solve the system of equations. 3x−4y%3D40 5x−5y%3D55 (1 point) Responses (8%2C−3) left parenthesis 8 comma negative 3 right parenthesis (14%2C 3) left parenthesis 14 comma 3 right parenthesis (18%2C 7) left parenthesis 18 comma 7 right parenthesis (4%2C−7)
To solve the system of equations, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
From the first equation, we have: 3x - 4y = 40 ----(1)
Solve this equation for x:
3x = 4y + 40
x = (4y + 40)/3 ----(2)
Substitute x in the second equation with the expression (4y + 40)/3:
5(4y + 40)/3 - 5y = 55
5(4y + 40) - 15y = 165
20y + 200 - 15y = 165
5y + 200 = 165
5y = -35
y = -7
Now, substitute the value of y in equation (2):
x = (4(-7) + 40)/3
x = (28 + 40)/3
x = 68/3
x = 22.67
Therefore, the solution to the system of equations is (22.67, -7).
To solve the system of equations:
3x - 4y = 40 ........(Equation 1)
5x - 5y = 55 ........(Equation 2)
We can use the method of substitution or elimination to solve the system.
Let's solve it using the method of substitution.
From Equation 1, isolate x:
3x - 4y = 40
3x = 4y + 40
x = (4/3)y + 40/3 ........(Equation 3)
Now substitute Equation 3 into Equation 2:
5x - 5y = 55
5((4/3)y + 40/3) - 5y = 55
(20/3)y + (200/3) - 5y = 55
(20/3 - 15/1)y = 55 - (200/3)
(20/3 - 45/3)y = (165 - 200/3) * 3/3
(-25/3)y = (495 - 200)/3
(-25/3)y = 295/3
Multiply both sides by -3/25:
y = (295/3) * (-3/25)
y = -885/75
y = -11.8
Now substitute the value of y back into Equation 3 to find x:
x = (4/3)y + 40/3
x = (4/3)(-11.8) + 40/3
x = -15.733 + 13.333
x = -2.4
Therefore, the solution to the system of equations is (x, y) = (-2.4, -11.8).
To solve the system of equations 3x - 4y = 40 and 5x - 5y = 55, you can use the method of substitution or elimination.
Let's solve it using the method of elimination:
Step 1: Multiply equation (1) by 5 and equation (2) by 3 to make the coefficients of 'x' the same:
Multiply equation (1) by 5: 5(3x - 4y) = 5(40) --> 15x - 20y = 200
Multiply equation (2) by 3: 3(5x - 5y) = 3(55) --> 15x - 15y = 165
So, the system of equations becomes:
15x - 20y = 200 (3)
15x - 15y = 165 (4)
Step 2: Now subtract equation (4) from equation (3) to eliminate 'x':
(15x - 20y) - (15x - 15y) = 200 - 165
15x - 20y - 15x + 15y = 35
-20y + 15y = 35
-5y = 35
Simplifying equation (5): -5y = 35
Dividing both sides by -5: y = -7
Step 3: Substitute the value of y = -7 into any one of the original equations, let's use equation (1) to solve for 'x':
3x - 4(-7) = 40
3x + 28 = 40
3x = 40 - 28
3x = 12
Dividing both sides by 3: x = 12/3 = 4
So, the solution to the system of equations is x = 4 and y = -7.
Therefore, the correct answer is option (4, -7).