Solving Systems of Equations with Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does substitution mean in the context of solving equations?

Back

Substitution is the process of replacing a variable in one equation with an equivalent expression from another equation.

Front

How do you solve a system of equations using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable. 4. Substitute back to find the first variable.

Front

What is the solution to a system of equations?

Back

The solution is the point (x, y) where the equations intersect, representing the values of the variables that satisfy all equations in the system.

Front

If x = 6, what is the value of y in the equation y = 2x - 3?

Back

y = 2(6) - 3 = 12 - 3 = 9.

Front

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

Back

Substitute y = 3 - x into the second equation: 3(3 - x) + x = 5.

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 do not intersect.

Front

What is the solution to the system: 2x + 8y = 20 and y = 2?

Back

Substituting y = 2 into the first equation gives 2x + 8(2) = 20, which simplifies to x = 2.

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: 5x - 2y = 3 and y = 2x?

Back

Substituting y = 2x into the first equation gives 5x - 2(2x) = 3, which simplifies to x = 3, y = 6.