solve the system equations

Question

-x+6y=13
4x-10y=-10

Answer 1

To solve this system of equations, we can use the method of substitution.

Step 1: Solve one equation for one variable in terms of the other variable.

Rearranging the first equation, we have:
-x + 6y = 13
⇒ -x = 13 - 6y
⇒ x = -13 + 6y

Step 2: Substitute the expression found for x into the second equation.

Substituting x = -13 + 6y into the second equation, we have:
4(-13 + 6y) - 10y = -10
-52 + 24y - 10y = -10
14y = 42
y = 42/14
y = 3

Step 3: Substitute the value of y back into one of the original equations to find the value of x.

Using the first equation:
-x + 6(3) = 13
-x + 18 = 13
-x = 13 - 18
-x = -5
x = 5

Therefore, the solution to the system of equations is x = 5 and y = 3.