Name:
Date:
Systems of Equations: Substitution Method
Solve each system of equations using the Substitution Method.
a)
b)
𝑦 = 5𝑥 − 7
−3𝑥 − 2𝑦 = −12
2𝑦 = 𝑥 + 3
𝑥=𝑦
Solution: ____________
Solution: ____________
Check first equation:
Check first equation:
Check second equation:
Check second equation:
c)
d)
𝑦 =𝑥−2
2𝑥 + 2𝑦 = 4
𝑦 = 3𝑥 + 6
𝑥 = 3𝑦 + 6
Solution: ____________
Solution: ____________
Check first equation:
Check first equation:
Check second equation:
Check second equation:
Name:
Date:
Review – Rock these.
a) Create a system of equations that contains
parallel lines.
b) Is the line x = 4 a function? Explain why or
why not.
c) Find the equation of the line between the
points (2, 7) and (-3, -8).
d) Find the equation of the line perpendicular
3
to 𝑦 = 4 𝑥 + 7 which passes through the point
(3, 5).
Equation of the line: _______________
e) Solve for x.
f) How many solutions does this system of
equations have?
-3(7 + x) = -2(x – 5)
𝑦 = −3𝑥 + 4
𝑦 = 3𝑥 − 5
No. of solutions: ________
How can you tell?
x = __________
g) Put this equation in slope-intercept form.
h) Does this system of equations contain
parallel lines, perpendicular lines, or neither?
6x – 4y – 9 = 0
2
𝑦 = 3𝑥 + 8
6 = 3𝑦 − 2𝑥
Parallel
Perpendicular
Neither
Name:
Date:
Answer Key
a)
b)
c)
d)
x = 2, y = 3
x = 3, y = 3
x = 2, y = 0
x = - 3, y = - 3
a) check your answer on Desmos!
b) No, because the same input (x) generates more than 1
output (y)
c) y = 3x + 1
−4
d) 𝑦 = 3 𝑥 + 9
e) x = – 31
f) The system has 1 solution. I can tell this because the
slopes of the 2 lines are different, therefore the lines
intersect at exactly 1 point.
3
9
g) 𝑦 = 2 𝑥 + 4
h) The lines are parallel.