What is the answer to this?

Question

1. Solve the system by substitution. Tell whether the system has one solution, infinitely many solutions, or no solutions.

4x + 2y = 7

y = -2x + 3.5

Answer 1

Hi Abby. By using substitution, we can “plug” the second equation into the first to solve for x.

The first equation will now read 4x + 2(-2x + 3.5) = 7

This gives you 4x -4x + 7 = 7

Now you have 0 + 7= 7, or 7 = 7.

There are infinitely many solutions.

Not only that, both equations have the point (0, 3.5) and (1, 1.5).

If you plot these points in each equation, you will see that.

Therefore, though the equations look different, every point for x and y will match. Both lines are exact.

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Answer 2

The technique of solving by substitution means you use one given equation to solve for one of the variables, and then substitute that variable into the other equation to make it a one-variable equation.

In this case, we're already given a solved equation, y = -2x + 3.5. This is an equation solved for y in terms of x. When solving for a variable, you'll want the target variable on only one side and everything else on the other.

Now for substitution: in the former equation, 4x + 2y = 7, replace all occurrences of y with -2x + 3.5. We c7n do this because we already know the relation y = -2x + 3.5.

4x + 2y = 7

4x + 2(-2x + 3.5) = 7

4x -4x + 7 = 7

7 = 7

This is our result. Because the statement 7 = 7 is true for ALL possible values of x and y, there are infinitely many solutions.