8-GG8 2024-25 Systems with Substitution

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

How do you determine which variable to solve for in substitution?

Back

Choose the variable that is easiest to isolate, often the one with a coefficient of 1 or -1.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

Solve for y in the equation: 7x + y = 19.

Back

y = 19 - 7x.

Front

If y = 3x - 5, what is y when x = 2?

Back

y = 3(2) - 5 = 1.

Front

What is the first step in solving the system: 5x - 2y = 3 and y = 2x?

Back

Substitute 2x for y in the first equation.

Front

What is the solution to the system: 3x + 2y = 16 and 7x + y = 19?

Back

No solution.

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if they hold true.

Front

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

Back

(1, -2).