System of equation.
Find the value of X
Y=3x+5
2y=4x+24
Please help with steps to solve this problem. Thank for your help.
Sorry, Ms. Sue. Noticed a mistake in the last line.
2(3x+5) = 4x + 24
6x + 10 = 4x + 24
2x = 14
x = 7
Y=3x+5
2y=4x+24
2(3x + 5) = 4x + 24
6x + 10 = 4x + 24
x = 14
Thanks, Matt.
Thank you so much Ms. Sue and Matt.
To find the value of x for the given system of equations, you can use the method of substitution or elimination.
1. Method of Substitution:
Step 1: Solve one of the equations for one variable in terms of the other variable.
In this case, let's solve the first equation for x in terms of y:
Y = 3x + 5
Subtract 5 from both sides:
Y - 5 = 3x
Divide both sides by 3:
(Y - 5) / 3 = x
Step 2: Substitute the expression for x in terms of y into the second equation.
In this case, substitute (Y - 5) / 3 for x in the second equation:
2y = 4((Y - 5) / 3) + 24
Step 3: Simplify and solve for y.
To simplify, multiply both sides by 3 to remove the fraction:
6y = 4(Y - 5) + 72
Distribute 4 to the terms inside the parentheses:
6y = 4Y - 20 + 72
Combine like terms:
6y = 4Y + 52
Subtract 4Y from both sides:
6y - 4Y = 52
Simplify:
2y = 52
Divide both sides by 2 to solve for y:
y = 52 / 2
y = 26
Step 4: Substitute the value of y back into the equation solved for x to find x:
x = (Y - 5) / 3
x = (26 - 5) / 3
Simplify:
x = 21 / 3
x = 7
Therefore, the value of x is 7 when y is 26 for the given system of equations.
2. Method of Elimination:
Step 1: Multiply both sides of the first equation by 2 to make the coefficients of y equal in both equations:
2Y = 6x + 10
Step 2: Rewrite the second equation so that the coefficients of y are the same:
2y = 4x + 24
Step 3: Subtract the equation from Step 2 from the equation of Step 1:
(2Y) - (2y) = (6x + 10) - (4x + 24)
Simplify:
0 = 2x - 14
Add 14 to both sides:
14 = 2x
Divide both sides by 2 to solve for x:
x = 14 / 2
x = 7
Step 4: Substitute the value of x back into either of the original equations to find y:
Y = 3x + 5
Y = 3(7) + 5
Simplify:
Y = 21 + 5
Y = 26
Again, the value of x is 7 when y is 26 for the given system of equations.