Math Problem Statement
Solve using elimination method
Solution
The image you provided contains a system of linear equations. Let's extract and solve it using the elimination method.
The equations visible in the image are:
1. \quad 3a - 2b - 36 &= 10 \\ 2. \quad 5a - 3b - 46 &= 4 \end{aligned}$$ First, let's rewrite these equations in standard form: $$\begin{aligned} 1. \quad 3a - 2b &= 46 \quad \text{(Adding 36 to both sides)} \\ 2. \quad 5a - 3b &= 50 \quad \text{(Adding 46 to both sides)} \end{aligned}$$ Now, we'll use the elimination method. To eliminate one variable, we'll multiply the first equation by 3 and the second equation by 2 so that the coefficients of $$b$$ will be opposites. $$\begin{aligned} 1. \quad 9a - 6b &= 138 \quad \text{(Multiplying the first equation by 3)} \\ 2. \quad 10a - 6b &= 100 \quad \text{(Multiplying the second equation by 2)} \end{aligned}$$ Next, subtract the second equation from the first: $$\begin{aligned} (9a - 6b) - (10a - 6b) &= 138 - 100 \\ - a &= 38 \end{aligned}$$ So, $$a = -38$$ Now, substitute $$a = -38$$ back into one of the original equations to solve for $$b$$. Using the first equation: $$3(-38) - 2b = 46$$ Simplify: $$-114 - 2b = 46$$ Add 114 to both sides: $$-2b = 160$$ Finally, divide by -2: $$b = -80$$ The solution to the system of equations is: $$\boxed{a = -38 \text{ and } b = -80}$$ Would you like more details on this solution, or do you have any questions? ### Relative Questions: 1. How does the elimination method compare to the substitution method in solving systems of equations? 2. Can you verify the solution by substituting the values of $$a$$ and $$b$$ back into both original equations? 3. What would be the next step if the coefficients of $$b$$ were not easily eliminated? 4. How does solving a system of equations graphically compare to the elimination method? 5. How can you apply the elimination method to a system of three equations with three variables? ### Tip: Always double-check your solutions by substituting the values back into the original equations to ensure they satisfy both equations.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Systems of linear equations
Elimination method
Formulas
-
Theorems
-
Suitable Grade Level
Grades 9-12
Related Recommendation
Solve a System of Linear Equations using the Elimination Method
Solve Systems of Linear Equations Using Elimination Method
Solve the System of Equations Using Elimination Method
Solving a System of Equations Using the Elimination Method: Step-by-Step Guide
Solve System of Equations using the Elimination Method