Solve each of these systems using the substitution method. Make sure to check your answers !
2x + 3y = -4
x - 2y = 5
Question 1 answers
x = 1, y = -2
x = -1, y = 2
x = 1, y = 2
x = -2, y = -1
x = 5 + 2y
2x + 3y = -4
Substitute 5 + 2y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
To solve the system of equations using the substitution method, follow these steps:
1. Choose one of the equations and solve it for one variable in terms of the other variable.
Let's choose the second equation, x - 2y = 5, and solve it for x:
x = 2y + 5
2. Substitute the expression we just found for the variable in the other equation.
Substitute x in the first equation with 2y + 5:
2(2y + 5) + 3y = -4
3. Simplify and solve the resulting equation for y.
4y + 10 + 3y = -4
7y + 10 = -4
7y = -4 - 10
7y = -14
y = -14 / 7
y = -2
4. Substitute the value of y back into the equation we used to solve for x to find the value of x.
x = 2(-2) + 5
x = -4 + 5
x = 1
5. Check the solution by substituting the values of x and y into both of the original equations.
For the first equation, 2x + 3y = -4:
2(1) + 3(-2) = -4
2 - 6 = -4
-4 = -4 (True)
For the second equation, x - 2y = 5:
1 - 2(-2) = 5
1 + 4 = 5
5 = 5 (True)
So, the solution to the system of equations is x = 1 and y = -2.