Solve the system of equations.
3x−4y=40
5x−5y=55 (1 point)
Responses
(8,−3)
left parenthesis 8 comma negative 3 right parenthesis
(18, 7)
left parenthesis 18 comma 7 right parenthesis
(14, 3)
left parenthesis 14 comma 3 right parenthesis
(4,−7)
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
From the first equation, we can solve for x:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3
Now substitute 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 = 165 - 200
5y = -35
y = -7
Now substitute y back into the first equation to solve for x:
3x - 4(-7) = 40
3x + 28 = 40
3x = 40 - 28
3x = 12
x = 12/3
x = 4
Therefore, the solution to the system of equations is (4, -7).
To solve the system of equations, we can use the method of substitution:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for x:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3
Step 2: Substitute the value of x from the first equation into the second equation.
5x - 5y = 55
5((4y + 40)/3) - 5y = 55
Multiplying both sides of the equation by 3 to get rid of the fraction:
15(4y + 40) - 15y = 165
60y + 600 - 15y = 165
45y + 600 = 165
45y = 165 - 600
45y = -435
y = -435/45
y = -9.67 (rounded to two decimal places)
Step 3: Substitute the value of y back into the equation to find x.
x = (4(-9.67) + 40)/3
x = (-38.68 + 40)/3
x = 1.32 (rounded to two decimal places)
Therefore, the solution to the system of equations is:
x = 1.32 and y = -9.67
or (1.32, -9.67)
To solve the system of equations, 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 in terms of the other variable.
Let's solve the first equation for x:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3
Step 2: Substitute the expression for x into the second equation.
Substituting (4y + 40)/3 for x in 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 = 165 - 200
5y = -35
y = -35/5
y = -7
Step 3: Substitute the value of y back into the expression for x to find its value.
x = (4y + 40)/3
x = (4(-7) + 40)/3
x = (-28 + 40)/3
x = 12/3
x = 4
Therefore, the solution to the system of equations is (4, -7).