Solve for x y=5x-7 , y=-22
The question is asking you to determine the value of the variable 'x' that satisfies both of the given linear equations simultaneously. The first equation is 'y = 5x - 7' and the second equation is 'y = -22'. By finding the value of 'x' that works for both equations, you will have solved for 'x'. This is a typical problem in algebra that involves solving a system of linear equations.
$y = 5 x - 7$,$y = - 22$
Answer
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:
Substitution: This is the process of replacing a variable with its value. In this case, we replace $y$ with $-22$.
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.
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.
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.
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.
