Question

Given these two separate systems, how would solving by elimination differ than substitution algebraically?

x + y = 7 4x + 9y = 20
2x + 6y = 5 3x – 9y = 1

A. Add the equations in the first system
B. Subtract the equations in the first system
C. Multiply one or both equations in the second system
D. Divide one or both equations in the second system

Answer 1

In solving systems of linear equations, elimination involves adjusting and combining the equations to remove one variable, while substitution involves solving one equation for one variable and inserting that into the other equation. Both require careful steps and rechecking for accuracy.

Step-by-step explanation:

Solving Systems of Linear Equations

To solve systems of equations, two common methods are elimination and substitution. When faced with the systems:

• x + y = 7
• 4x + 9y = 20

and

• 2x + 6y = 5
• 3x – 9y = 1

The difference between solving by elimination and substitution is that with elimination, you adjust the equations so you can add or subtract them to remove one variable. For the first system, you can Add the equations (Option A) or Subtract the equations (Option B) after altering them if necessary. For the second system, you may need to Multiply or Divide one or both equations (Options C and D) to get coefficients that will eliminate a variable when combined.

With substitution, you solve one equation for a single variable, and then substitute that expression in place of the variable in the other equation. This eventually isolates one variable, allowing you to solve for it and substitute back to find the other.

Algebraically, elimination may involve adding or subtracting multiples of the equations, while substitution involves inserting an expression for one variable into another equation. Both methods require careful checking and rechecking at each step to ensure accurate solutions.