Solve the simultaneous linear equation of x+2y=7, 2x+y=2
since x = 7-2y,
2(7-2y)+y = 2
Solve for y, and then get x
I wanted the full solving
I want the full solving
To solve the simultaneous linear equation x + 2y = 7 and 2x + y = 2, we can use the method of substitution or the method of elimination.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for y:
2x + y = 2
y = 2 - 2x
Step 2: Substitute the expression for the variable found in Step 1 into the other equation, and solve for the remaining variable.
Substituting y = 2 - 2x into the first equation:
x + 2(2 - 2x) = 7
x + 4 - 4x = 7
-3x + 4 = 7
-3x = 7 - 4
-3x = 3
x = 3 / (-3)
x = -1
Step 3: Substitute the value found in Step 2 back into one of the original equations and solve for the other variable.
Substituting x = -1 into the first equation:
-1 + 2y = 7
2y = 7 + 1
2y = 8
y = 8 / 2
y = 4
So, the solution to the simultaneous linear equations x + 2y = 7 and 2x + y = 2 is x = -1 and y = 4.
Method 2: Elimination
Step 1: Multiply one or both of the equations by constants such that the coefficients of one variable in both equations become opposites.
In this case, we'll multiply the first equation by 2 and the second equation by -1:
2(x + 2y) = 2(7)
-1(2x + y) = -1(2)
Simplifying, we get:
2x + 4y = 14
-2x - y = -2
Step 2: Add the two equations together to eliminate one variable.
(2x + 4y) + (-2x - y) = 14 + (-2)
2x - 2x + 4y - y = 12
3y = 12
y = 12 / 3
y = 4
Step 3: Substitute the value found in Step 2 back into one of the original equations and solve for the other variable.
Substituting y = 4 into the first equation:
x + 2(4) = 7
x + 8 = 7
x = 7 - 8
x = -1
So, the solution to the simultaneous linear equations x + 2y = 7 and 2x + y = 2 is x = -1 and y = 4.