Solve Systems by Substitution

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves 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 = -4x + 5?

Back

To solve for y, simply substitute any value of x into the equation. For example, if x = 1, then y = -4(1) + 5 = 1.

Front

What does it mean if two lines represented by a system of equations intersect?

Back

If two lines intersect, it means that the system of equations has one unique solution, which is the point of intersection.

Front

What is the first step in solving the system of equations y = 3x - 16 and y = -4x + 5 by substitution?

Back

The first step is to set the two equations equal to each other since both equal y: 3x - 16 = -4x + 5.

Front

What is the solution to the system of equations y = -4x + 5 and y = 3x - 16?

Back

The solution is (3, -7).

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the solution back into both original equations to see if both equations are satisfied.

Front

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

Back

It indicates that the lines are parallel and will never intersect.

Front

What is the significance of the coefficients in a system of linear equations?

Back

The coefficients determine the slope and position of the lines represented by the equations.

Front

How can you express y in terms of x from the equation 3x + 2y = 13?

Back

Rearranging gives y = (13 - 3x)/2.

Front

What is the solution to the system of equations y = 4x + 1 and 3x + 2y = 13?

Back

The solution is (1, 5).