Math Problem Statement
What is the solution to y=1/2x-3 and 2x-3y=6
Solution
We are given the system of two linear equations:
To solve for the values of and , we can use substitution. Since the first equation already expresses in terms of , we can substitute this expression for into the second equation.
Step 1: Substitute into .
Step 2: Simplify the equation.
Distribute the on the left side:
Step 3: Combine like terms.
Now, the equation becomes:
Step 4: Solve for .
Subtract 9 from both sides:
Now multiply both sides by 2 to eliminate the fraction:
Step 5: Substitute into the first equation to find .
Using the equation :
Final Solution:
The solution to the system of equations is:
Would you like a more detailed explanation or help with other questions?
Related Questions:
- How can you solve a system of equations using the elimination method?
- What is the graphical interpretation of the solution to a system of linear equations?
- How do you check the solution to a system of equations?
- What is the slope-intercept form of a linear equation, and how is it used?
- Can a system of equations have no solution or infinitely many solutions?
Tip:
When solving systems of equations, always check your solution by substituting the values back into the original equations to confirm they satisfy both equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Substitution Method
Formulas
y = (1/2)x - 3
2x - 3y = 6
Theorems
Substitution method for solving systems of linear equations
Suitable Grade Level
Grades 8-10
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