1.)Solve for y in the following system of equations.
x + 4y = -38
-x - 6y = 58
My answer 1.) -10
2.) 6
3.) 12
4.) 10
2.)Solve for y in the following system of equations.
x - 10y = -50
-4x + 6y = -4
1.) -6
2.)3
3.)-3
My answer4.)6
To solve a system of equations, you can use either the substitution method or the elimination method. I will explain both methods, and then we can solve the given systems of equations together.
1.) Substitution method:
Step 1: Solve one equation for one variable in terms of the other variable.
In this case, let's solve the first equation for x in terms of y:
x = -38 - 4y
Step 2: Substitute this expression for x into the second equation:
-(-38 - 4y) - 6y = 58
38 + 4y - 6y = 58
-2y = 20
y = -10
So, the solution for y in the first system of equations is -10.
2.) Elimination method:
Step 1: Multiply the equations by appropriate coefficients such that adding or subtracting them eliminates one of the variables.
For this system, we don't need to multiply any equations since the coefficients of x and y are already opposites in the second equation.
Step 2: Add or subtract the equations to eliminate one variable.
(x + 4y) + (-x - 6y) = (-38) + 58
-2y = 20
y = -10
Again, the solution for y in the second system of equations is -10.
So, for question 1, the correct answer is option 1.) -10.
And for question 2, the correct answer is option 1.) -10.
Please double-check your answers to make sure they match the correct solution.