SME
Grade 9 Math · Problem type
Solve ax + by = c for y
Use this for “Solve 2x + 3y = 12 for y. What is y when x = 3?”
Chart
y-intercept (0, 4)
f(3) = 2
This is an example. Type your own values to start a new problem.
a
x
+
b
y
=
c
y
=
m
x
+
k
Splitting y = (c − ax) ÷ b gives y = mx + k, with slope m = −a ÷ b and y-intercept k = c ÷ b.
x
Point’s x
example
y
Point’s y
calculated
Formulas
a
×
x
+
b
×
y
=
c
2 × 3 + 3 × 2 = 12
Assumptions
•
Treat x as a number you know and undo what is done to y.
•
Take ax from both sides, then divide every term by b: y = (c − ax) ÷ b.
•
The points (x, y) that make it true lie on one straight line.
Step-by-step
WE KNOW
x = 3, a = 2, b = 3, c = 12
FIND
point’s y (y)
Step 1 · Find point’s y (y)
Use a × x + b × y = c
Take
ax
from
both
sides,
then
divide
both
sides
by
b
.
y
=
c
−
a
×
x
b
y
=
12 − 2 × 3
3
y
=
12 − 6
3
y
=
6
3
y
=
2
→
solved
for
y
:
y
=
12 − 2
x
3
Check
Put the numbers back in. Both sides should match.
2 × 3 + 3 × 2 = 12 ✓
Topic check
See what you know: 5 questions on this topic
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