Solve the system of linear equations by substitution.
{
−
2
x
+
y
=
4
3
x
+
y
=
9
(
2
,
6
)
(
1
,
8
)
(
1
,
6
)
(
3
,
5
)
To solve the system of linear equations by substitution, we first solve one of the equations for one variable and then substitute that expression into the other equation.
Given equations:
1) -2x + y = 4
2) 3x + y = 9
From equation 1, we can isolate y:
y = 2x + 4
Now substitute this expression for y into equation 2:
3x + (2x + 4) = 9
5x + 4 = 9
5x = 5
x = 1
Now substitute x = 1 back into one of the original equations to find y:
-2(1) + y = 4
-2 + y = 4
y = 6
Therefore, the solution to the system of equations is x = 1 and y = 6.
So, the correct answer is option (1,6).