Math Problem Statement

are these solved by elimination or substitution

Are these solved by elimination or substitution?

Solution

In the image you provided, the two systems of equations are asking to be solved using substitution and elimination methods.

Solve by Substitution:

For the first system of equations:

  • x+3y=7x + 3y = 7
  • 2x+3y=112x + 3y = 11

This system is more straightforward to solve by substitution, as you can express one variable in terms of the other (for example, solve the first equation for xx in terms of yy and substitute that into the second equation).

Solve by Elimination:

For the second system of equations:

  • 3x2y=73x - 2y = -7
  • 2x+5y=82x + 5y = 8

This system is more straightforward to solve by elimination. You can manipulate the equations to eliminate one of the variables by adding or subtracting them after multiplying each equation by an appropriate factor.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Substitution Method
Elimination Method

Formulas

Substitution method: Solve for one variable in terms of another and substitute it into the other equation.
Elimination method: Add or subtract equations after appropriate multiplication to eliminate one variable.

Theorems

Linear equations theorem: Solutions exist at the intersection of lines if they intersect.

Suitable Grade Level

Grades 8-10