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Solve Systems of Equations by Substitution: example 5.20 · Physics Playground

Exercises Systems of equations

Example 5.20 from Elementary Algebra, 5.2 Solve Systems of Equations by Substitution

Solve Systems of Equations by Substitution: example 5.20

Solve the system by substitution. ${\begin{matrix} 5 x - 2 y = −10 \\ y = \frac{5}{2} x \end{matrix}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The second equation is already solved for y, so we can substitute for y in the first equation.

Substitute x for y in the first equation.

Replace the y with $\frac{5}{2} x .$

Solve for x.

Since 0 = −10 is a false statement the equations are inconsistent. The graphs of the two equation would be parallel lines. The system has no solutions.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the system by substitution. ${\begin{matrix} 3 x + 2 y = 9 \\ y = - \frac{3}{2} x + 1 \end{matrix}$

How did it go?

PreviousSolve Systems of Equations by Substitution: example 5.19 Next Solve Systems of Equations by Substitution: example 5.21

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 5.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Substitute x for y in the first equation.
Replace the y with $\frac{5}{2} x .$
Solve for x.

Solution

Your turn