Question

Solve each pair of equations by substituting


2x + y = 3
4x + 3y = 1

Answer 1

Step: Solve
2
x
+
y
=
3
for y:
2
x
+
y
=
3
2
x
+
y
+
−
2
x
=
3
+
−
2
x
(Add -2x to both sides)
y
=
−
2
x
+
3

Step: Substitute
−
2
x
+
3
for
y
in
4
x
+
3
y
=
1
:
4
x
+
3
y
=
1
4
x
+
3
(
−
2
x
+
3
)
=
1
−
2
x
+
9
=
1
(Simplify both sides of the equation)
−
2
x
+
9
+
−
9
=
1
+
−
9
(Add -9 to both sides)
−
2
x
=
−
8
−
2
x
−
2
=
−
8
−
2
(Divide both sides by -2)
x
=
4

Step: Substitute
4
for
x
in
y
=
−
2
x
+
3
:
y
=
−
2
x
+
3
y
=
(
−
2
)
(
4
)
+
3
y
=
−
5
(Simplify both sides of the equation)

Answer:
x
=
4
and
y
=
−
5

Answer 2

the value of x and y is 4 and -5 respectively.

Explanation:

from the equation we say let;

2x + y = 3 .............. equation 1

4x + 3y = 1.............. equation 2

from equation 1

2x + y = 3 .............. equation 1

y = 3 - 2x................ equation 3

Substitute for y in equation 2

4x + 3y = 1.............. equation 2

we have,

4x + 3(3- 2x) = 1

4x + 9 -6x = 1

we have to collect the like terms

9-1 = 6x -4x

8 = 2x

divide both sides by 2

8/2 = 2x/2

4 = x

therefore x = 4

put x = 4 in equation 3

y = 3 - 2x................ equation 3

y = 3 - 2(4)

y = 3 -8

y = -5

therefore the value of x and y is 4 and -5 respectively.

to check if your answer is correct, put the value of x and y in any of the equations.

2x + y = 3 .............. equation 1

2(4) + (-5) = 3

8 -5 = 3

3 = 3......................... proved