solve this system of equations
2x-3y=7
3x+y=16
Multiply the second equation by 3, to create a +3y term, and then add that to the first equation, to eliminate the y variable.
2x -3y = 7
9x +3y = 48
11x = 55
x = 5
3y = 2x -7 = 10 - 7 = 3
y = 1
2X-3Y=7
3+Y=16
YOU HELPPED ME ME BUT I RELLY DON'T KNOW HOW TO DO THAT ON MY OWEN MY TECHERS JUST GIVE ME TEST AND DON'T SHOW ME HOW TO DO IT CAN U SHOW ME STEP BE STEP HOW
To solve this system of equations, you can use the method of substitution or the method of elimination. I will explain both methods, and you can choose which one you prefer.
Method 1: Substitution
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for y:
3x + y = 16
y = 16 - 3x
Step 2: Substitute the expression for y into the other equation.
Substitute y in the first equation:
2x - 3(16 - 3x) = 7
Step 3: Simplify and solve for x.
2x - 48 + 9x = 7
11x - 48 = 7
11x = 55
x = 55/11
x = 5
Step 4: Substitute the value of x back into one of the original equations to find y.
Using the first equation:
2(5) - 3y = 7
10 - 3y = 7
-3y = 7 - 10
-3y = -3
y = -3/(-3)
y = 1
The solution to the system of equations is x = 5 and y = 1.
Method 2: Elimination
Step 1: Multiply one or both equations by suitable constants to make the coefficients of one variable the same or additive inverses.
In this case, multiplying the first equation by 3 and the second equation by 2 will give us the same coefficient for y.
Multiplying the first equation by 3:
6x - 9y = 21
Multiplying the second equation by 2:
6x + 2y = 32
Step 2: Add or subtract the equations to eliminate one variable.
Subtracting the first equation from the second equation:
(6x + 2y) - (6x - 9y) = 32 - 21
6x + 2y - 6x + 9y = 11y = 11
11y = 11
y = 11/11
y = 1
Step 3: Substitute the value of y back into one of the original equations to find x.
Using the first equation:
2x - 3(1) = 7
2x - 3 = 7
2x = 7 + 3
2x = 10
x = 10/2
x = 5
So the solution to the system of equations is x = 5 and y = 1.