Use substitution to solve the system.
3x+5y=21
y=2x-1
3x+5y=21
3x + 5(2x - 1) = 21
3x + 10x - 5 = 21
13x - 26
x = 2
Substitute 2 for x in the second problem to find the value of y.
To use substitution to solve the system, we will substitute the value of y from the second equation into the first equation.
Given:
1) 3x + 5y = 21
2) y = 2x - 1
Step 1: Substitute the value of y from equation 2 into equation 1.
Substitute (2x - 1) in place of y in equation 1:
3x + 5(2x - 1) = 21
Step 2: Simplify the equation by distributing the 5 to both terms inside the parentheses.
3x + 10x - 5 = 21
Step 3: Combine like terms on the left side of the equation.
3x + 10x - 5 = 21
13x - 5 = 21
Step 4: Add 5 to both sides of the equation to isolate the term with x.
13x - 5 + 5 = 21 + 5
13x = 26
Step 5: Divide both sides of the equation by 13 to solve for x.
13x/13 = 26/13
x = 2
Step 6: Substitute the value of x back into either equation to solve for y. Let's use equation 2.
y = 2x - 1
y = 2(2) - 1
y = 4 - 1
y = 3
Therefore, the solution to the system of equations is x = 2 and y = 3.