Question

I have a system of equations I don’t remember how to do :|

I forgot how to solve this, and I forgot how to find the slope…

Answer 1

There are infinite numbers of solution.

Step-by-step explanation:

Question :

`\begin{gathered}\begin{gathered}\begin{gathered}\small\begin{cases}\sf{x + y= \bf{3}} \\ \\ \sf{3x + 3y= \bf{9}}\end{cases} \end{gathered}\end{gathered}\end{gathered}`

Solution :

Solving the question and finding the final answer.

Here,

• x + y = 3 . . . (i)
• 3x + 3y = 9 . . . (ii)

━━━━━━━━━

Now, from equation (i),

`\twoheadrightarrow{\sf{x + y = 3}}`

`\twoheadrightarrow{\sf{x = 3 - y}}`

━━━━━━━━━

Now, putting the value of x in equation (ii)

`\begin{gathered} \qquad{\longrightarrow{\sf{3x + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{3(3 - y) + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 3y + 3y = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 0 = 9}}} \\ \\ \qquad{\longrightarrow{\sf{9 - 0 = 9}}} \\ \\ \qquad{\longrightarrow{\sf{\underline{\underline{\red{9 = 9}}}}}}\end{gathered}`

This statement is true for all values of x and y.

So, there are infinite numbers of solution.

`\underline{\rule{220pt}{3pt}}`

Answer 2

x + y = 3 (infinite solutions)

Explanation:

You observe that all of the numbers in the second equation are multiples of 3. When you divide the second equation by 3, it becomes identical to the first equation. The equations are said to be "dependent."

That means both equations graph as the same line, so will intersect at every point on the line. The system of equations has an infinite number of solutions.

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Additional comments

There are a number of ways to solve a system of equations. Two methods commonly taught are "substitution" and "elimination". Either one works here.

We can solve the first equation for y by subtracting x from both sides:

x +y -x = 3 -x

y = -x +3 . . . . . . simplify

In this form, the slope is the coefficient of x. Here, it is -1.

This expression for y can be substituted into the other equation:

3x +3(-x +3) = 9

3x -3x +9 = 9 . . . . . eliminate parentheses

9 = 9 . . . . . . . . . . . simplify

This is true for all values of x or y. There are an infinite number of solutions.