Question

Solve the following systems of equations algebraically. Write your answer in the form of (x, y).

y = 3x + 5 and y = x + 19

Answer 1

Let's solve your system by substitution.
y
=
3
x
+
5
;
y
=
x
+
19

Step: Solve
y
=
3
x
+
5
for y:
y
=
3
x
+
5

Step: Substitute
3
x
+
5
for
y
in
y
=
x
+
19
:
y
=
x
+
19
3
x
+
5
=
x
+
19
3
x
+
5
+
−
x
=
x
+
19
+
−
x
(Add -x to both sides)
2
x
+
5
=
19
2
x
+
5
+
−
5
=
19
+
−
5
(Add -5 to both sides)
2
x
=
14
2
x
2
=
14
2
(Divide both sides by 2)
x
=
7

Step: Substitute
7
for
x
in
y
=
3
x
+
5
:
y
=
3
x
+
5
y
=
(
3
)
(
7
)
+
5
y
=
26
(Simplify both sides of the equation)

Answer:
x
=
7
and
y
=
26