Substitution Method for Solving Systems of Linear Equations

What is the primary goal when solving a system of linear equations using the substitution method?

• To find the slope of the lines

• To determine the y-intercept

• To find the point of intersection

• To calculate the area between the lines

In the substitution method, what is the first step when both equations are already solved for the same variable?

• Add the equations together

• Substitute one equation into the other

• Multiply the equations

• Graph the equations

When substituting y = 2x + 3 into y = 5x, what is the resulting equation?

• 2x + 3 = 5

• 2x + 3 = 5x

• 5x = 3

• 2x = 5x + 3

After finding x = 1 in the first example, how do you find the value of y?

• Graph the equations to find y

• Substitute x = 1 into both equations

• Substitute x = 1 into y = 2x + 3

• Substitute x = 1 into y = 5x

What is the solution to the system of equations y = x - 4 and y = 4x - 10?

• (2, -2)

• (3, 1)

• (1, 5)

• (0, 0)

In the second example, what is the value of x after solving the equation?

• x = 1

• x = 0

• x = 2

• x = 3

In the third example, what is the first step after substituting x = y - 1 into 2x - y = 6?

• Solve for y

• Solve for x

• Graph the equation

• Add the equations

What is the solution to the system of equations 2x - y = 6 and x = y - 1?

• (0, 0)

• (1, 5)

• (2, -2)

• (7, 8)

In the third example, what is the value of y after solving the equation?

• y = 8

• y = 6

• y = 4

• y = 2

What is the final step in solving a system using the substitution method?

• Check the solution by substituting back into the original equations

• Add the equations

• Verify the solution graphically

• Multiply the equations