Solve the system of equations.
x=6y−3
2x+7y=13
To solve the system of equations, we can substitute the value of x from the first equation into the second equation:
2x + 7y = 13
2(6y-3) + 7y = 13
12y - 6 + 7y = 13
19y - 6 = 13
19y = 19
y = 1
Now substitute the value of y back into the first equation to find x:
x = 6y - 3
x = 6(1) - 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.
To solve the system of equations, we can use the substitution method.
Step 1: Solve the first equation for x
x = 6y - 3
Step 2: Substitute the value of x into the second equation
2(6y - 3) + 7y = 13
Step 3: Simplify and solve for y
12y - 6 + 7y = 13
19y - 6 = 13
19y = 13 + 6
19y = 19
y = 19/19
y = 1
Step 4: Substitute the value of y back into the first equation to find x
x = 6(1) - 3
x = 6 - 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 1.
To solve the given system of equations, we will use the method of substitution. Follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we have x = 6y - 3.
Step 2: Substitute the expression obtained from step 1 into the other equation.
Replace x in the second equation with 6y - 3.
2(6y - 3) + 7y = 13
Step 3: Simplify and solve the resulting equation.
Distribute the 2:
12y - 6 + 7y = 13
Combine like terms:
19y - 6 = 13
Add 6 to both sides:
19y = 19
Divide both sides by 19:
y = 1
Step 4: Substitute the solution from step 3 into either of the original equations to find the value of the other variable.
Using the first equation: x = 6(1) - 3 = 6 - 3 = 3
So, the solution to the system of equations is x = 3 and y = 1.