Systems of Equations - Algebra

When we add the two equations, the and variables cancel leaving us with:

which means there is no solution for this system.

Rewriting the equation as , we can see there are four terms we are working with, so factor by grouping is an appropriate method. Between the first two terms, the Greatest Common Factor (GCF) is and between the third and fourth terms, the GCF is 4. Thus, we obtain . Setting each factor equal to zero, and solving for , we obtain from the first factor and from the second factor. Since the square of any real number cannot be negative, we will disregard the second solution and only accept .

Add 8 to both sides to set the equation equal to 0:

To factor, find two integers that multiply to 24 and add to 10. 4 and 6 satisfy both conditions. Thus, we can rewrite the quadratic of three terms as a quadratic of four terms, using the the two integers we just found to split the middle coefficient:

Then factor by grouping:

Set each factor equal to 0 and solve:

and

Rewriting the equation as , we can see there are four terms we are working with, so factor by grouping is an appropriate method. Between the first two terms, the Greatest Common Factor (GCF) is and between the third and fourth terms, the GCF is 4. Thus, we obtain . Setting each factor equal to zero, and solving for , we obtain from the first factor and from the second factor. Since the square of any real number cannot be negative, we will disregard the second solution and only accept .

First factor the expression by pulling out :

Factor the expression in parentheses by recognizing that it is a difference of squares:

Set each term equal to 0 and solve for the x values:

Eliminate parentheses, then write this quadratic equation in standard form, with all nonzero terms on one side:

Now factor the quadratic expression using the -method - split the middle term into two terms whose coefficients add up to 11 and have product . These numbers are

Set each factor to 0:

Rewriting the equation as , we can see there are four terms we are working with, so factor by grouping is an appropriate method. Between the first two terms, the Greatest Common Factor (GCF) is and between the third and fourth terms, the GCF is 4. Thus, we obtain . Setting each factor equal to zero, and solving for , we obtain from the first factor and from the second factor. Since the square of any real number cannot be negative, we will disregard the second solution and only accept .

First factor the expression by pulling out :

Factor the expression in parentheses by recognizing that it is a difference of squares:

Set each term equal to 0 and solve for the x values:

Rewriting the equation as , we can see there are four terms we are working with, so factor by grouping is an appropriate method. Between the first two terms, the Greatest Common Factor (GCF) is and between the third and fourth terms, the GCF is 4. Thus, we obtain . Setting each factor equal to zero, and solving for , we obtain from the first factor and from the second factor. Since the square of any real number cannot be negative, we will disregard the second solution and only accept .

First factor the expression by pulling out :

Factor the expression in parentheses by recognizing that it is a difference of squares:

Set each term equal to 0 and solve for the x values:

Eliminate parentheses, then write this quadratic equation in standard form, with all nonzero terms on one side:

Now factor the quadratic expression using the -method - split the middle term into two terms whose coefficients add up to 11 and have product . These numbers are

Set each factor to 0:

Add 8 to both sides to set the equation equal to 0:

To factor, find two integers that multiply to 24 and add to 10. 4 and 6 satisfy both conditions. Thus, we can rewrite the quadratic of three terms as a quadratic of four terms, using the the two integers we just found to split the middle coefficient:

Then factor by grouping:

Set each factor equal to 0 and solve:

and

First factor the expression by pulling out :

Factor the expression in parentheses by recognizing that it is a difference of squares:

Set each term equal to 0 and solve for the x values:

Eliminate parentheses, then write this quadratic equation in standard form, with all nonzero terms on one side:

Now factor the quadratic expression using the -method - split the middle term into two terms whose coefficients add up to 11 and have product . These numbers are

Set each factor to 0:

Add 8 to both sides to set the equation equal to 0:

To factor, find two integers that multiply to 24 and add to 10. 4 and 6 satisfy both conditions. Thus, we can rewrite the quadratic of three terms as a quadratic of four terms, using the the two integers we just found to split the middle coefficient:

Then factor by grouping:

Set each factor equal to 0 and solve:

and

First factor the expression by pulling out :

Factor the expression in parentheses by recognizing that it is a difference of squares:

Set each term equal to 0 and solve for the x values:

Add 8 to both sides to set the equation equal to 0:

To factor, find two integers that multiply to 24 and add to 10. 4 and 6 satisfy both conditions. Thus, we can rewrite the quadratic of three terms as a quadratic of four terms, using the the two integers we just found to split the middle coefficient:

Then factor by grouping:

Set each factor equal to 0 and solve:

and

First factor the expression by pulling out :

Factor the expression in parentheses by recognizing that it is a difference of squares:

Set each term equal to 0 and solve for the x values:

Eliminate parentheses, then write this quadratic equation in standard form, with all nonzero terms on one side:

Now factor the quadratic expression using the -method - split the middle term into two terms whose coefficients add up to 11 and have product . These numbers are

Set each factor to 0:

Add 8 to both sides to set the equation equal to 0:

To factor, find two integers that multiply to 24 and add to 10. 4 and 6 satisfy both conditions. Thus, we can rewrite the quadratic of three terms as a quadratic of four terms, using the the two integers we just found to split the middle coefficient:

Then factor by grouping:

Set each factor equal to 0 and solve:

and