use subsitution system to solve
4x+5y=21
Y=3x-11
4x+5y=21
Y=3x-11
4x + 5(3x - 11) = 21
4x + 15x - 55 = 21
19x = 21 + 55
19x = 76
x = 4
y = (3 * 4) - 11
y = 1
To solve the system of equations using the substitution method, we will substitute the expression for y in terms of x from the second equation into the first equation. Here's how:
Given equations:
1) 4x + 5y = 21
2) y = 3x - 11
Step 1: Start with the second equation and substitute y with its value from equation 2 into equation 1:
4x + 5(3x - 11) = 21
Step 2: Simplify the equation:
4x + 15x - 55 = 21
19x - 55 = 21
Step 3: Add 55 to both sides to remove the constant term on the left side:
19x - 55 + 55 = 21 + 55
19x = 76
Step 4: Divide both sides by 19 to solve for x:
19x/19 = 76/19
x = 4
Step 5: Substitute the value of x back into equation 2 to solve for y:
y = 3(4) - 11
y = 12 - 11
y = 1
Step 6: The solution to the system of equations is x = 4 and y = 1.
Therefore, the solution to the system of equations is x = 4 and y = 1.