Lesson 13 (1 & 2) Solving Systems of Equations by 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 solving equations?

Back

Substitution is a method of solving a system of equations by solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you solve for y in the equation y = 2x + 1?

Back

To solve for y, simply substitute any value of x into the equation. For example, if x = 1, then y = 2(1) + 1 = 3.

Front

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

Back

The solution is (6, 9). Substitute x = 6 into the second equation: y = 2(6) - 3 = 12 - 3 = 9.

Front

What is the first step in solving the system of equations: y = 2x + 1 and y = 4x - 1?

Back

Set the two equations equal to each other: 2x + 1 = 4x - 1.

Front

What is the solution to the system of equations: y = 8 and y = -4x + 4?

Back

The solution is (-1, 8). Substitute y = 8 into the second equation: 8 = -4x + 4, which gives x = -1.

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 do not intersect.

Front

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

Back

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

Front

How do you find the x-value in the equation 2y + x = -15 when y = -3?

Back

Substitute y = -3 into the equation: 2(-3) + x = -15, which simplifies to x = -9.

Front

What is the solution to the system of equations: 2y + x = -15 and x = 3y?

Back

The solution is (-9, -3). Substitute x = 3y into the first equation to find y.