29 M1 Review

Front

Which graph represents the equation 2x + 4y = 12?

Back

To find the graph, rearrange the equation into slope-intercept form (y = mx + b). The equation can be rewritten as y = -0.5x + 3. The graph will have a y-intercept at (0, 3) and a slope of -0.5.

Front

Solve the equation: 3x + 15 = 3(x + 5)

Back

Infinitely Many Solutions. The equation simplifies to 3x + 15 = 3x + 15, which is always true.

Front

What is the solution to the equation 2x + 3 = 2x + 5?

Back

No Solution. The equation simplifies to 3 = 5, which is false.

Front

Solve the system of equations: y = 2x and x + y = 9. What are the values of x and y?

Back

(3, 6). Substitute y = 2x into the second equation to find x, then substitute back to find y.

Front

Solve for x: -6x = 30

Back

x = -5. Divide both sides by -6.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variables that can satisfy the equation.

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

How do you find the y-intercept of a linear equation?

Back

Set x = 0 in the equation and solve for y.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

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