Solve the system by substitution.x-5y=2 ,2x+3y=17
solve the first one to say
x = 5y+2, now sub that into the second
2(5y+2) + 3y = 17
solve for y, sub that back into x = 5y+2
To solve the given system of equations by substitution, we can follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Step 2: Substitute the expression found in step 1 into the other equation.
Step 3: Solve the resulting equation for the remaining variable.
Step 4: Substitute the value found in step 3 back into one of the original equations to find the value of the other variable.
Step 5: Write the solution as an ordered pair (x, y).
Let's begin with step 1:
From equation 1: x - 5y = 2
Let's solve this equation for x:
x = 2 + 5y
Now, we'll move to step 2:
Substitute the expression for x (found in step 1) into the second equation:
2x + 3y = 17
2(2 + 5y) + 3y = 17
Simplifying the equation further:
4 + 10y + 3y = 17
13y + 4 = 17
13y = 17 - 4
13y = 13
y = 13/13
y = 1
Now, let's proceed to step 4:
Substitute the value of y, which is 1, into one of the original equations (equation 1):
x - 5(1) = 2
x - 5 = 2
x = 2 + 5
x = 7
Hence, the solution to the given system of equations is x = 7 and y = 1. Therefore, the solution is (7, 1).