solve the system of equations:
3x + 2y = 17
2x - y = 9
4x+2y=9 and 2x+4y=10
To solve the system of equations:
Step 1: We will use the method of substitution. First, solve one equation for one variable in terms of the other variable. We can solve the second equation for y:
2x - y = 9
- y = 9 - 2x
y = 2x - 9
Step 2: Substitute the value of y in terms of x into the other equation:
3x + 2(2x - 9) = 17
3x + 4x - 18 = 17
7x - 18 = 17
Step 3: Simplify the equation:
7x = 17 + 18
7x = 35
Step 4: Solve for x:
x = 35 / 7
x = 5
Step 5: Substitute the value of x back into one of the original equations to solve for y. Using the first equation:
3x + 2y = 17
3(5) + 2y = 17
15 + 2y = 17
Step 6: Simplify the equation:
2y = 17 - 15
2y = 2
Step 7: Solve for y:
y = 2 / 2
y = 1
Therefore, the solution to the system of equations is x = 5 and y = 1.
To solve this system of equations, we will use the method of substitution.
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the second equation for y:
2x - y = 9
Add y to both sides of the equation:
2x - 9 = y
Step 2: Substitute the expression for y in the first equation.
3x + 2(2x - 9) = 17
Simplify:
3x + 4x - 18 = 17
7x - 18 = 17
Step 3: Solve for x.
Add 18 to both sides of the equation:
7x = 35
Divide both sides by 7:
x = 5
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Let's use the second equation:
2x - y = 9
Substitute x = 5:
2(5) - y = 9
10 - y = 9
Subtract 10 from both sides:
-y = -1
Multiply both sides by -1 to solve for y:
y = 1
Therefore, the solution to the system of equations is x = 5 and y = 1.
Double the second equation and add them.
3x + 2y = 17
4x - 2y = 18
____________
7x = 35
Take it from there. Divide both sides by 7 and plug the answer you get for x into either equation, to get y.