Solve the system of equations.
3x−4y=40
5x−5y=55 (1 point)
Responses
(18, 7)
left parenthesis 18 comma 7 right parenthesis
(8,−3)
left parenthesis 8 comma negative 3 right parenthesis
(4,−7)
left parenthesis 4 comma negative 7 right parenthesis
(14, 3)
left parenthesis 14 comma 3 right parenthesis
To solve the system of equations, we can use the method of substitution or elimination.
Method of substitution:
From the first equation, we have 3x - 4y = 40. Solving for x, we get x = (40 + 4y)/3.
Substituting this into the second equation:
5((40 + 4y)/3) - 5y = 55.
Multiplying both sides by 3 to get rid of the fractions:
5(40 + 4y) - 15y = 165.
Expanding and simplifying:
200 + 20y - 15y = 165.
5y = 165 - 200.
5y = -35.
y = -35/5.
y = -7.
Substituting this value of y back into the first equation:
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:
1. Begin by multiplying the first equation by 5 and the second equation by 3 to eliminate the y variable.
This gives us:
Equation 1: 15x - 20y = 200
Equation 2: 15x - 15y = 165
2. Now subtract Equation 2 from Equation 1 (15x - 20y - (15x - 15y) = 200 - 165).
Simplifying this equation, we get:
-20y + 15y = 35
-5y = 35
y = -7
3. Substitute the value of y (-7) back into either equation. Let's use Equation 1:
3x - 4(-7) = 40
3x + 28 = 40
4. Simplify and solve for x:
3x = 40 - 28
3x = 12
x = 4
Therefore, the solution to the system of equations is (4, -7).
To solve the system of equations, we can use either the substitution method or the elimination method. Let's use the elimination method here.
Step 1: Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations the same.
5 * (3x - 4y) = 5 * 40
3 * (5x - 5y) = 3 * 55
Simplifying these equations gives us:
15x - 20y = 200
15x - 15y = 165
Step 2: Now we can eliminate x by subtracting the second equation from the first equation.
(15x - 20y) - (15x - 15y) = 200 - 165
-20y + 15y = 35
-5y = 35
y = -7
Step 3: Substitute the value of y back into one of the original equations 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 x = 4 and y = -7. So, the correct option is (4, -7).