Solve using substitution: 1. y = -7x + 8 2. y = -6x + 6
Understand the Problem
The question is asking us to solve a system of equations using the substitution method. The given equations are linear equations in terms of y and x, and we will need to substitute one equation into the other to find the values of the variables.
Answer
The solution to the system of equations is $x = 2$ and $y = -6$.
Answer for screen readers
The solution to the system of equations is $x = 2$ and $y = -6$.
Steps to Solve
- Set the equations equal to each other
Since both equations are equal to $y$, we can set them equal to each other: $$ -7x + 8 = -6x + 6 $$
- Isolate the variable
Next, we isolate $x$ by moving $-6x$ to the left side and $8$ to the right side: $$ -7x + 6x = 6 - 8 $$
- Simplify the equation
This simplifies to: $$ -x = -2 $$
- Solve for x
Now, we can solve for $x$: $$ x = 2 $$
- Substitute x back into one of the original equations
We can substitute $x = 2$ back into the first equation to find $y$: $$ y = -7(2) + 8 $$
- Calculate y
Now, simplify: $$ y = -14 + 8 = -6 $$
- Final solution
Thus, the solution to the system of equations is $x = 2$ and $y = -6$.
The solution to the system of equations is $x = 2$ and $y = -6$.
More Information
This solution represents the point where the two lines defined by the equations intersect, which is $(2, -6)$. Substitution is a handy method for solving systems of linear equations, especially when one equation can easily be expressed in terms of the other.
Tips
- Neglecting to isolate the variable correctly: Always ensure to correctly rearrange the equation before solving for the variable.
- Incorrect substitution: Double-check that you are substituting the correct value of $x$ into the equation.
- Arithmetic errors: Be careful when performing calculations, especially when combining like terms or adding/subtracting.
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