Question

Solve by substitution.

-6x+5y=1
6x+4y=-10?
Please show all work.

Answer 1

Add the two equations.

9y = 1 - 10

Answer 2

I agree

Answer 3

Yea

Answer 4

-6x+5y=1

6x+4y=-10
________
9y=-9
y=-1

6x+4(-1)=-10
6x-4=-10
6x=-6
x=-1

So x=-1 and y=-1

Answer 5

using substitution, as requested,

-6x+5y=1
so y = (6x+1)/5
so using that in the other equation,
6x+4y=-10
6x + 4(6x+1)/5 = -10
30x + 24x + 4 = -50
54x = -54
x = -1
y = (6(-1)+1)/5 = -1

Answer 6

[AI-generated answer — Explain Bot]

To solve the system of equations by substitution, we follow these steps:

Step 1: Solve one of the equations for one variable in terms of the other variable.
Step 2: Substitute the expression from Step 1 into the other equation.
Step 3: Solve the resulting equation for the remaining variable.
Step 4: Substitute the value found in Step 3 back into one of the original equations to solve for the other variable.
Step 5: Write the solution as an ordered pair (x, y), where x and y are the values found in Steps 3 and 4.

Let's apply these steps to solve the given system of equations:

Equation 1: -6x + 5y = 1
Equation 2: 6x + 4y = -10

Step 1: Solve Equation 1 for x:
-6x + 5y = 1
-6x = 1 - 5y
x = (1 - 5y)/(-6)

Step 2: Substitute the expression for x from Step 1 into Equation 2:
6x + 4y = -10
6((1 - 5y)/(-6)) + 4y = -10

Step 3: Simplify and solve for y:
(1 - 5y) + 4y = -10 (Multiplying both sides by -6 to simplify the equation)
1 - y = -10
-y = -11
y = 11

Step 4: Substitute y = 11 back into Equation 1 and solve for x:
-6x + 5(11) = 1
-6x + 55 = 1
-6x = 1 - 55
-6x = -54
x = -54/(-6)
x = 9

Step 5: Write the solution as an ordered pair (x, y):
Therefore, the solution is (9, 11).

As a result, the system of equations -6x + 5y = 1 and 6x + 4y = -10 can be solved by substitution, and the solution is (9, 11).