x-5y=-21
9y-8x=44
substitution method
x-5y=-21
9y-8x=44
x = 5y - 21
9y - 8(5y - 21) = 44
9y - 40y + 168 = 44
-31y = 44 - 168
-31y = -124
y = 4
Take it from there.
x = 5y -21
9y-8(5y-21) = 44
9y -40y +168 = 44
-31y + 168 = 44
-31y + 168 -168 = 44 -168
-31y = -124
y = 4
x = 5(4)-21 = -1
(-1, 4)
The substitution method is a way to solve a system of equations by isolating one variable in one equation and substituting it into the other equation. Here's how you can use the substitution method to solve the given system of equations:
1. Start with the given system of equations:
Equation 1: x - 5y = -21
Equation 2: 9y - 8x = 44
2. From Equation 1, isolate x by adding 5y to both sides:
x = -21 + 5y
3. Substitute the value of x in Equation 2 with -21 + 5y:
9y - 8(-21 + 5y) = 44
4. Simplify Equation 2 by distributing -8 to both terms inside the parentheses:
9y + 168 - 40y = 44
5. Combine like terms by subtracting 168 and 44 from both sides of the equation:
9y - 40y = 44 - 168
-31y = -124
6. Divide both sides of the equation by -31 to solve for y:
y = -124 / -31
y = 4
7. Now that we have the value of y, substitute it back into Equation 1 to solve for x:
x - 5(4) = -21
x - 20 = -21
8. To isolate x, add 20 to both sides of the equation:
x = -21 + 20
x = -1
9. The solution to the system of equations is x = -1 and y = 4.
To check if these values are correct, substitute them back into the original equations and ensure that both equations hold true.