Solve for x y=5x-7 , y=-22

Solution:

Step 1: Substitute $y$ with $-22$ in the equation

Step 1.1: Perform the substitution in the equation $y=5x-7$

$$-22=5x-7$$ $$y=-22$$

Step 1.2: Simplify the equation

Step 1.2.1: Eliminate any grouping symbols

$$-22=5x-7$$ $$y=-22$$ $$-22=5x-7$$ $$y=-22$$ $$-22=5x-7$$ $$y=-22$$

Step 2: Solve the simplified equation for $x$

$$x=-3,y=-22$$

Knowledge Notes:

To solve a system of equations where one variable is already isolated, such as $y=5x-7$, and you are given a value for $y$, you can substitute the given value into the equation to find the corresponding value of $x$. This process involves the following knowledge points:

1. Substitution: This is the process of replacing a variable with its value. In this case, we replace $y$ with $-22$.

2. Simplifying Equations: After substitution, the equation may need to be simplified. This involves performing arithmetic operations and rearranging terms to isolate the variable of interest.

3. Solving Linear Equations: The given equation is linear, and solving for $x$ involves isolating $x$ on one side of the equation. This typically requires moving terms from one side of the equation to the other and performing inverse operations.

4. Linear Equations: These are equations of the first degree, meaning that the variable $x$ is not raised to any power higher than one. The general form is $ax+b=c$, where $a$, $b$, and $c$ are constants.

5. Systems of Equations: A system of equations is a set of two or more equations with the same variables. In this case, the system is simple because the second equation directly gives the value of $y$.

In this problem, we are given a system of equations with one equation already solved for $y$. By substituting the given value of $y$ into the other equation, we can solve for $x$. This is a straightforward application of substitution in solving systems of equations.