Virginia SOL Math / Algebra I / Equations & Inequalities

A.EI.2

Systems of Equations

What you'll learn

  • Solve systems of two linear equations by graphing
  • Solve systems by substitution and elimination
  • Interpret the solution of a system in context

Words to know

System —
two or more equations solved together
Solution of a system —
an ordered pair that makes both equations true
Substitution —
replace one variable using the other equation
Elimination —
add or subtract equations to remove a variable
Intersection —
the point where two lines cross
Consistent —
a system that has at least one solution

Why it matters Systems find the point where two conditions meet at once, such as when two pricing plans cost the same.

Worked examples

Model ItI do

Solve the system by graphing: y = x + 1 and y = -x + 5.

Graph both lines. They cross at (2, 3), and that point satisfies both equations, so the solution is (2, 3).

Try It TogetherWe do

Solve by substitution: y = 2x and x + y = 6.

Substitute 2x for y: x + 2x = 6, so 3x = 6 and x = 2. Then y = 2(2) = 4. The solution is (2, 4).

Now YouYou do

Solve by elimination: x + y = 10 and x - y = 4.

Add the two equations to eliminate y, then solve. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Where do y = 3 and x = 5 intersect?

  2. 2.Solve by substitution: y = x + 1 and y = 4.

  3. 3.Two lines that cross at exactly one point have how many solutions?

On Level

The core Quick Check from the book.

  1. 1.Is (3, 1) a solution of y = x - 2? Answer yes or no.

  2. 2.Solve by substitution: y = x + 2 and y = 5.

  3. 3.Solve by elimination: x + y = 8 and x - y = 2.

  4. 4.Two lines that never cross have how many solutions?

  5. 5.Where do y = 4 and x = 2 intersect?

Challenge

Stretch your thinking.

  1. 1.Solve by elimination: 2x + y = 11 and x - y = 1.

  2. 2.Solve by substitution: y = 2x - 3 and x + y = 9.

  3. 3.A system whose two equations graph the same line has how many solutions?