Solutions by Substitution Flashcards

The substitution method for solving two-order systems involves solving one equation using the terms of the other equation.

What is the result when substituting y = x + 1 into the equation 2x + y = 7?

What is the resulting equation after substituting y = x - 1 into 3x - y = 2?

What is the solution for the system 5x - 6y = 0 and y = x?

What is the solution for the system x - y = 6 and x = y + 2?

What is the solution for the system 10x - 10y = 1 and x = y - 3?

What is the solution for the system 5x - 2y = 6 and x = 5 - y?

What is the solution for the system x + y = 6 and 2x + y = 4?

What is the solution for the system 5x - 6 = y and 2x - 3y = 4?

What is the solution for the system 7x - 2 = 2y and 3x = 2y - 1?

What is the solution for the system 8x = 2y + 5 and 3x = y + 7?

What is the solution for the system 8y - 1 = x and 3x = 2y?

What is the solution for the system 7 + 2y = 8x and 3x - 2y = 0?

Are the equations 2x - y = c and x + 2y = d intersecting, parallel, or coincident?

Are the equations bx - ay = 2 and ax + by = 3 intersecting, parallel, or coincident?

Given that the value of b can never be equal to -1, are the equations x + y = ab and bx - y = a intersecting, parallel, or coincident?

Substitution Method Overview

The substitution method solves systems of equations by expressing one variable in terms of another and substituting it into a different equation.

Examples of Substitution in Equations

For equations 2x + y = 7 and y = x + 1, substituting y yields 3x + 1 = 7.
In equations 3x - y = 2 and y = x - 1, substitution produces 2x + 1 = 2.

Specific Solutions

For 5x - 6y = 0 and y = x, the solution is (0, 0).
The equations x - y = 6 and x = y + 2 have no solution indicating parallel lines.
The system 10x - 10y = 1 and x = y - 3 also has no solution.

Further Substitution Results

Substituting into 5x - 2y = 6 and x = 5 - y yields the solution (16/7, 19/7).
The system x + y = 6 and 2x + y = 4 gives the solution (-2, 8).

Additional Solutions

For equations 5x - 6 = y and 2x - 3y = 4, the solution is (14/13, -8/13).
The equations 7x - 2 = 2y and 3x = 2y - 1 result in the solution (3/4, 13/8).
Solving 8x = 2y + 5 and 3x = y + 7 yields (-9/2, -41/2).

Final Solutions from Substitution

For 8y - 1 = x and 3x = 2y, the result is (1/11, 3/22).
The system 7 + 2y = 8x and 3x - 2y = 0 has the solution (7/5, 21/10).

Identifying Equation Relationships

Equations of the form 2x - y = c and x + 2y = d are identified as intersecting.
For bx - ay = 2 and ax + by = 3, the equations are also intersecting.
Given that b ≠ -1 in the equations x + y = ab and bx - y = a, they are classified as intersecting.

These flashcards cover the substitution method for solving two-variable systems of equations. Each card presents equations and asks for the results of substituting one expression into another, helping you master this technique. Test your understanding and improve your algebra skills with these engaging flashcards.