how to substitute 3x+y=11
4x-5y= -22
y = (11 - 3 x)
4 x - 5 (11 - 3 x) = -22
4 x - 55 + 15 x = -22
19 x = - 77 etc
To solve a system of linear equations like these, you can use the method of substitution. Here's how you can solve these equations step by step:
Step 1: Solve one of the equations for one variable in terms of the other.
From the first equation, 3x + y = 11, we can isolate y by subtracting 3x from both sides:
y = 11 - 3x
Step 2: Substitute the expression obtained from step 1 into the other equation.
Replace y in the second equation, 4x - 5y = -22, with the expression we found:
4x - 5(11 - 3x) = -22
Step 3: Simplify and solve for x.
Distribute -5 into the parentheses:
4x - 55 + 15x = -22
Combine like terms on the left side:
19x - 55 = -22
Add 55 to both sides:
19x = -22 + 55
19x = 33
Divide both sides by 19 to solve for x:
x = 33/19
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Using the first equation, substitute x with 33/19:
3(33/19) + y = 11
Multiply through by 19 to get rid of the fraction:
99 + 19y = 209
Subtract 99 from both sides:
19y = 209 - 99
19y = 110
Divide both sides by 19 to solve for y:
y = 110/19
So the solution to the system of equations is x = 33/19 and y = 110/19.