Solutions to Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

Front

What does it mean for a point to be a solution to a linear equation?

Back

A point (x, y) is a solution to a linear equation if, when the x and y values are substituted into the equation, the equation holds true.

Front

How do you find the value of y in the equation 3x + y = 5 when x = 1?

Back

Substitute x = 1 into the equation: 3(1) + y = 5. This simplifies to 3 + y = 5, so y = 2.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the y-intercept of the equation y = 2x - 1?

Back

The y-intercept is -1, which is the value of y when x = 0.

Front

How can you determine if a point is a solution to the equation y = 2x - 1?

Back

Substitute the x-value of the point into the equation and see if the resulting y-value matches the y-value of the point.

Front

What is the solution to the equation 3y - 2x = -3 when x = 6?

Back

Substituting x = 6 gives 3y - 2(6) = -3, which simplifies to 3y - 12 = -3. Thus, 3y = 9, so y = 3.

Front

Is (5, 5) a solution to the equation x + y = 12?

Back

No, because substituting x = 5 and y = 5 gives 5 + 5 = 10, which does not equal 12.

Front

What is the solution to the equation y - 12 = x when x = 0?

Back

Substituting x = 0 gives y - 12 = 0, so y = 12.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set.