Prerequisites: Algebra Review

Self Check Systems of Equations Self Check

Now, you try. Complete the self-check activity by looking at the questions below, working them out, and then clicking on the question to review the solution.

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Solve the following system of equations for the two unknown values.

the equation y equals six x minus eleven and the equation negative two x minus three y equals negative seven

Note the first equation is already solved for y in terms of x so all you need to do is substitute the first equation into the second and solve.

Substitute the first equation into the second and solve.
negative two x minus three times the quantity six x minus eleven end quantity equals negative seven, negative two x minus eighteen x plus thirty three equals negative seven, negative twenty x equals negative forty, x equals two
Substitute the answer to the previous step into one of the original problems.
y equals six times two minus eleven, y equals twelve minus eleven, y equals one

The answers are x = 2 and y = 1. You can substitute these values back into the equations to check your work.

 

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Solve the following system of equations for the two unknown values.

the equation y equals negative three x plus five and the equation five x minus four y equals negative three

Note the first equation is already solved for y in terms of x so all you need to do is substitute the first equation into the second and solve.

Substitute the first equation into the second and solve.
five x minus four times the quantity of negative three x plus five end quantity equals negative three, five x plus twelve x minus twenty equals negative three, seventeen x equals seventeen, x equals one
Substitute the answer to the previous step into one of the original problems.
y equals negative three times one plus five, y equals negative three plus five, y equals two

The answers are x = 1 and y = 2. You can substitute these values back into the equations to check your work.

 

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Solve the following system of equations for the two unknown values.

the equation negative seven x minus two y equals negative thirteen and the equation x minus two y equals eleven

To solve for the unknowns, first solve the second equation for x in terms of y, then substitute into the first equation. Then use that solution to find the value of the second unknown.

Solve for x in terms of y in the second equation.
x minus two y equals eleven, x minus two y plus two y equals eleven plus two y, x equals eleven plus two y
Substitute the answer from the previous step into the first equation and solve.
negative seven times the quantity eleven plus two y end quantity minus two y equals negative thirteen, negative seventy seven minus fourteen y minus two y equals negative thirteen, negative seventy seven minus sixteen y equals negative thirteen, negative sixteen y equals sixty four, negative sixteen y divided by negative sixteen equals sixty four divided by negative sixteen, y equals negative four
Substitute the answer from the previous step into one of the equations (choose the simpler of the two equations).
x minus two times negative four equals eleven, x plus eight equals eleven, x equals three

The answers are x = 3 and y = 4. You can substitute these values back into the equations to check your work.