U6L2 Opener Testing Solutions in an Equation

Front

What is the process to determine if a value is a solution to an equation?

Back

To determine if a value is a solution to an equation, substitute the value into the equation and simplify. If both sides of the equation are equal, then the value is a solution.

Front

What does it mean for a value to satisfy an equation?

Back

A value satisfies an equation if, when substituted into the equation, it makes the equation true (both sides equal).

Front

How do you check if y=4 is a solution for the equation 3y^2 + 2y - 4 = 0?

Back

Substitute y=4 into the equation: 3(4)^2 + 2(4) - 4 = 48 + 8 - 4 = 52, which does not equal 0. Therefore, y=4 is not a solution.

Front

What is the solution to the equation 2x + 3 = 8?

Back

To find the solution, isolate x: 2x = 8 - 3; 2x = 5; x = 5/2 or 2.5. Therefore, x=2 does not satisfy the equation.

Front

How can you determine if y=4 is a solution for the equation 4y - 5 = 11?

Back

Substitute y=4 into the equation: 4(4) - 5 = 16 - 5 = 11, which is true. Therefore, y=4 is a solution.

Front

What is the method to verify if x=3 makes the equation 3x - 4 = 5 true?

Back

Substitute x=3 into the equation: 3(3) - 4 = 9 - 4 = 5, which is true. Therefore, x=3 is a solution.

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means that the discriminant (b^2 - 4ac) is less than zero, indicating that the graph of the equation does not intersect the x-axis.

Front

What is the significance of the discriminant in solving quadratic equations?

Back

The discriminant helps determine the nature of the roots of a quadratic equation: if it's positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

How do you solve the equation 9y^2 + 4y - 6 = -14 for y = -2?

Back

Substitute y = -2 into the equation: 9(-2)^2 + 4(-2) - 6 = 36 - 8 - 6 = 22, which does not equal -14. Therefore, y = -2 is not a solution.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.