Solve each linear equation by substitution.
{3x-2y=3
-x+2y=7
The answer is suppose to be (5,6)
To solve this system of linear equations by substitution, follow these steps:
Step 1: Solve one equation for one variable.
Let's solve the second equation for x in terms of y:
-x + 2y = 7
-x = -2y + 7
x = 2y - 7
Step 2: Substitute the expression for x in terms of y into the other equation.
Replace x in the first equation with 2y - 7:
3x - 2y = 3
3(2y - 7) - 2y = 3
6y - 21 - 2y = 3
4y - 21 = 3
4y = 3 + 21
4y = 24
y = 24/4
y = 6
Step 3: Substitute the value found for y back into one of the original equations to find x.
Using the first equation, substitute y = 6:
3x - 2(6) = 3
3x - 12 = 3
3x = 3 + 12
3x = 15
x = 15/3
x = 5
Therefore, the solution to the system of linear equations is (5, 6).