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### Solving Systems of Equations by Substitution To solve the given system of equations using substitution, follow these steps: **System of Equations:** 1. \( 4x + 3y = -25 \) 2. \( y = 6x + 43 \) **Instructions:** 1. Substitute the expression for \( y \) from Equation 2 into Equation 1. 2. Simplify and solve for \( x \). 3. Substitute the value of \( x \) back into Equation 2 to find \( y \). 4. Check the solution in both original equations. **Choices:** - One solution: Solve to see if the system has a single unique solution. - No solution: If the equations are parallel, they have no intersection. - Infinite number of solutions: If the equations are identical, there are infinite solutions. **Interactive Section:** - An input box is provided to enter the solution if one exists. - Options include selecting "One solution," "No solution," or "Infinite number of solutions." - Click the "Submit Question" button after entering your answer. By solving this system, you can determine if the lines intersect at a single point, have no intersection, or overlap completely.

### Solving Systems of Equations by Substitution To solve the given system of equations using substitution, follow these steps: **System of Equations:** 1. \( 4x + 3y = -25 \) 2. \( y = 6x + 43 \) **Instructions:** 1. Substitute the expression for \( y \) from Equation 2 into Equation 1. 2. Simplify and solve for \( x \). 3. Substitute the value of \( x \) back into Equation 2 to find \( y \). 4. Check the solution in both original equations. **Choices:** - One solution: Solve to see if the system has a single unique solution. - No solution: If the equations are parallel, they have no intersection. - Infinite number of solutions: If the equations are identical, there are infinite solutions. **Interactive Section:** - An input box is provided to enter the solution if one exists. - Options include selecting "One solution," "No solution," or "Infinite number of solutions." - Click the "Submit Question" button after entering your answer. By solving this system, you can determine if the lines intersect at a single point, have no intersection, or overlap completely.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Solving Systems of Equations by Substitution To solve the given system of equations using substitution, follow these steps: **System of Equations:** 1. \( 4x + 3y = -25 \) 2. \( y = 6x + 43 \) **Instructions:** 1. Substitute the expression for \( y \) from Equation 2 into Equation 1. 2. Simplify and solve for \( x \). 3. Substitute the value of \( x \) back into Equation 2 to find \( y \). 4. Check the solution in both original equations. **Choices:** - One solution: Solve to see if the system has a single unique solution. - No solution: If the equations are parallel, they have no intersection. - Infinite number of solutions: If the equations are identical, there are infinite solutions. **Interactive Section:** - An input box is provided to enter the solution if one exists. - Options include selecting "One solution," "No solution," or "Infinite number of solutions." - Click the "Submit Question" button after entering your answer. By solving this system, you can determine if the lines intersect at a single point, have no intersection, or overlap completely.
Transcribed Image Text:### Solving Systems of Equations by Substitution To solve the given system of equations using substitution, follow these steps: **System of Equations:** 1. \( 4x + 3y = -25 \) 2. \( y = 6x + 43 \) **Instructions:** 1. Substitute the expression for \( y \) from Equation 2 into Equation 1. 2. Simplify and solve for \( x \). 3. Substitute the value of \( x \) back into Equation 2 to find \( y \). 4. Check the solution in both original equations. **Choices:** - One solution: Solve to see if the system has a single unique solution. - No solution: If the equations are parallel, they have no intersection. - Infinite number of solutions: If the equations are identical, there are infinite solutions. **Interactive Section:** - An input box is provided to enter the solution if one exists. - Options include selecting "One solution," "No solution," or "Infinite number of solutions." - Click the "Submit Question" button after entering your answer. By solving this system, you can determine if the lines intersect at a single point, have no intersection, or overlap completely.
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