Study · algebra · system of equations
Stop here, understand this
Welcome back, Maya. You stopped here yesterday on step 2. We're going to walk through it together — no shame, no rush. Three more steps after this.
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42 min · 1 quiz
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Solve this system for x and y
Given:
Find values of x and y that satisfy both equations.
You said yesterday that step 2 was confusing — "I get the idea but I keep losing track of which variable I'm replacing." We'll slow down here.
2x + 3y = 12 and x − y = 1
Find values of x and y that satisfy both equations.
You said yesterday that step 2 was confusing — "I get the idea but I keep losing track of which variable I'm replacing." We'll slow down here.
1
Pick the easier equation to isolate a variable
You picked
x − y = 1. Good — it has small coefficients. Solving for x gives you x = y + 1.2
Substitute the expression into the OTHER equation
Take x = y + 1 and put it in place of x in the first equation:
2(y + 1) + 3y = 12. The point of substitution is that the second equation can now talk about only one variable — y. (This is the part you said felt confusing — it's just "replace one letter with what it equals from the other line.")3
Simplify and solve for y
Distribute the 2, combine like terms, and solve for y.
4
Plug y back in to find x
Use your expression from step 1 to get x.
5
Check the answer in both equations
Always check both — that's how you know it's right and not just plausible.
Why this matters context
Substitution is the bridge from "two unknowns" to "one unknown." Once you can rewrite one variable as the other, you've turned a 2D problem into a 1D problem. Every other technique (elimination, matrices) is a faster version of the same idea.
Visual from BlackBoard
two lines meet at one point · that's the solution
Where this is going path
STEP 2 OF 5SESSION 2/4
After this set, you'll move into elimination (1 session), then a small quiz mixing both methods, then onto 3-variable systems. That sequence usually unlocks the rest of Algebra II for you.
SO
SOPHIA · AGENT · TUTOR · 14:36
Hey Maya — I noticed you re-read step 1 three times. That's totally fine. The thing that actually trips most students up isn't substitution itself, it's losing track of which variable you replaced. Try saying out loud: "I'm replacing x with y+1, so now the equation is about y only." If it still doesn't click, ping me
@sophia and we'll do a worked example side-by-side.Learning path · Algebra II12 modules · 4 done · 1 current
M01
Linear equations review
y = mx + b · slope-intercept
M02
Inequalities
graphing · interval notation
M03
Absolute value
equations & inequalities
M04
Functions intro
domain · range · notation
M05
Systems · 2 vars
substitution · elimination · graphing
M06
Systems · 3 vars
matrices intro
M07
Polynomials
factoring · degree
M08
Quadratics
formula · completing the square