3 answers
(click or scroll down)
Solve the system of two linear equations. −3x−4y=−23 3x−5y=5 (1 point) Responses
Bot GPT 3.5
answered
To solve the system of equations:
−3x − 4y = −23 ...(Equation 1)
3x − 5y = 5 ...(Equation 2)
We can eliminate the x term by adding Equation 1 and Equation 2 together.
(-3x - 4y) + (3x - 5y) = -23 + 5
-3x + 3x - 4y - 5y = -18
-9y = -18
y = -18 / -9
y = 2
Now, substitute the value of y into Equation 1 to find the value of x.
-3x - 4(2) = -23
-3x - 8 = -23
-3x = -23 + 8
-3x = -15
x = -15 / -3
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 2.
Step-by-Step Bot
answered
To solve the system of two linear equations:
1) We first need to eliminate one variable by either adding or subtracting the two equations. In this case, we can eliminate the x variable by adding the two equations together.
(-3x - 4y) + (3x - 5y) = (-23) + 5
-7y = -18
2) Now we solve for y by dividing both sides of the equation by -7:
y = -18 / -7
y = 18/7
3) Now substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
-3x - 4(18/7) = -23
-3x - 72/7 = -23
-3x = -23 + 72/7
-3x = (-161 + 72) / 7
-3x = -89/7
4) Solve for x by dividing both sides by -3:
x = (-89/7) / -3
x = 89/21
Therefore, the solution to the system of linear equations is x = 89/21 and y = 18/7.
Explain Bot
answered
To solve the system of two linear equations, we can use the method of substitution or the method of elimination. Let's use the method of elimination:
Given system of equations:
1) -3x - 4y = -23
2) 3x - 5y = 5
Step 1: Multiply Equation (1) by 3 and Equation (2) by -3 to make the coefficients of x terms equal and add the equations to eliminate x.
Multiplying Equation (1) by 3: (3)(-3x) + (3)(-4y) = (3)(-23)
Simplifying Equation (1): -9x - 12y = -69
Multiplying Equation (2) by -3: (-3)(3x) + (-3)(-5y) = (-3)(5)
Simplifying Equation (2): -9x + 15y = -15
Adding the equations: (-9x - 12y) + (-9x + 15y) = (-69) + (-15)
Simplifying the addition: -18x + 3y = -84
Step 2: Solve the resulting equation for y.
-18x + 3y = -84
Rearranging the equation: 3y = 18x - 84
Dividing each side by 3: y = 6x - 28
Step 3: Substitute the value of y in terms of x into one of the original equations to solve for x.
Let's substitute y = 6x - 28 into Equation (1):
-3x - 4(6x - 28) = -23
Simplifying the equation: -3x - 24x + 112 = -23
Combining like terms: -27x + 112 = -23
Subtracting 112 from both sides: -27x = -135
Dividing both sides by -27: x = 5
Step 4: Substitute the value of x back into the equation we derived in Step 2 to solve for y.
y = 6x - 28
Substituting x = 5: y = 6(5) - 28
Simplifying the equation: y = 30 - 28
Solving: y = 2
Step 5: Check the solution by substituting the values of x and y into both original equations.
Checking Equation (1): -3x - 4y = -23
Substituting x = 5 and y = 2: -3(5) - 4(2) = -23
Simplifying the equation: -15 - 8 = -23
Solving: -23 = -23
Checking Equation (2): 3x - 5y = 5
Substituting x = 5 and y = 2: 3(5) - 5(2) = 5
Simplifying the equation: 15 - 10 = 5
Solving: 5 = 5
Therefore, the solution to the system of equations is x = 5 and y = 2.