On Level Sub Work 2/20 - System of Equations--Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does substitution mean in the context of solving equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into another equation.

Front

Solve for y: y = 3x + 5 when x = 2.

Back

y = 3(2) + 5 = 6 + 5 = 11.

Front

What is the first step in solving a system of equations using substitution?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

If y = 4x + 1, what is y when x = -1?

Back

y = 4(-1) + 1 = -4 + 1 = -3.

Front

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

Back

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

Front

Solve: y = 2x + 3 and y = -x + 1 using substitution.

Back

Set 2x + 3 = -x + 1. Solve for x: 3x = -2, x = -2/3. Substitute x back to find y: y = 2(-2/3) + 3 = 5/3. Solution: (-2/3, 5/3).

Front

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

Back

Substituting y in the first equation gives: 2x + 3(2x - 4) = 6. Solve for x: 8x - 12 = 6, 8x = 18, x = 9/4. Substitute x back to find y: y = 2(9/4) - 4 = 1/2. Solution: (9/4, 1/2).

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines on a coordinate plane, which represent the solutions to the system.

Front

If the equations are y = 3x + 2 and y = 3x - 1, what can be said about their solutions?

Back

The equations represent parallel lines, so there is no solution.