Solving Systems of Linear Equations by Substitution

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

• To find the intersection point of the lines

• To find the slope of the lines

• To eliminate one variable completely

• To graph the equations

In the first example, what is the first step in the substitution method?

• Multiply the equations by a constant

• Solve one equation for x or y

• Add the equations together

• Graph the equations

After substituting the expression for x in the first example, what is the next step?

• Solve for y

• Check the solution

• Graph the result

• Multiply by a constant

In the second example, what is the initial step taken to solve for y?

• Add x to both sides

• Divide by a constant

• Multiply by a constant

• Subtract y from both sides

What is the purpose of multiplying the entire equation by -1 in the second example?

• To find the slope

• To change the sign of each term

• To simplify the equation

• To eliminate a variable

In the third example, why is each term divided by three?

• To graph the equation

• To find the slope

• To eliminate a variable

• To simplify the coefficients

What is the result of substituting y = 0 into the equation in the third example?

• x = 1

• x = 0

• x = 6

• x = -6

What is the final step in verifying the solution of a system of equations?

• Graph the equations

• Add the equations together

• Substitute the values back into the original equations

• Multiply the equations by a constant

What is the main advantage of using the substitution method?

• It eliminates all variables

• It is faster than graphing

• It provides an exact solution

• It requires no calculations

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