1. What is the first step for solving this system by substitution? 3x-2y=8

Question

1. What is the first step for solving this system by substitution? 3x-2y=8

x+7y=10

2. How many solutions does this system of equations have? 3y-6x=12
y-2x=4

Answer 1

#1

I would isolate the x in the second equation,
that is, x = 10-7y
then substitute into the first equation.

#2
an infinite number of solutions, since the first equation is simply 3 times the second.

Answer 2

1. The first step for solving the system of equations by substitution is to solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:

x + 7y = 10
x = 10 - 7y

Now we have x in terms of y.

2. To determine the number of solutions for the system of equations, we need to determine whether the two equations are parallel, intersect at a single point, or coincide (represent the same line).

Let's examine the coefficients of x and y for both equations:

For the first equation: 3x - 2y = 8, the coefficient of x is 3 and the coefficient of y is -2.
For the second equation: y - 2x = 4, the coefficient of x is -2 and the coefficient of y is 1.

Since the coefficients are different for both equations, these equations represent two non-parallel lines. Therefore, this system of equations has a single point of intersection, and it has a unique solution.

Answer 3

1. The first step for solving a system of equations by substitution is to solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:

x + 7y = 10

Subtract 7y from both sides:

x = 10 - 7y

Now we have one equation (3x - 2y = 8) and the expression for x in terms of y (x = 10 - 7y). We can substitute this expression into the first equation to solve for y.

2. To determine the number of solutions for a system of equations, we need to compare the number of variables and the number of equations.

In this system:
Equation 1: 3y - 6x = 12
Equation 2: y - 2x = 4

Both equations have two variables (x and y) and two equations, which means it is possible to find a unique solution for x and y that satisfies both equations. This system has one solution.