How to solve this 5x-19=2y,3y+18=4x
5x-19=2y
3y+18=4x
5x-2y=19
4x-3y=18
15x-6y=57
8x-6y=36
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7x=21
and so on
why a separate cryptic post just saying "substitution method"?
5x-19=2y, so y = (5x-19)/2
3y+18=4x
3(5x-19)/2+18=4x
15x-57+36=8x
7x = 21
x = 3
y = (5*3-19)/2 = -2
SOLVING
4x + 6y = 21
7x - 3y = 3
To solve the system of equations 5x - 19 = 2y and 3y + 18 = 4x, we can use the method of substitution. Here's how to do it step by step:
Step 1: Solve one equation for one variable in terms of the other variable. Let's solve the first equation for y:
5x - 19 = 2y
Divide both sides of the equation by 2 to isolate y:
(5x - 19) / 2 = y
Step 2: Substitute the expression for y from the first equation into the second equation:
3((5x - 19) / 2) + 18 = 4x
Step 3: Simplify the equation by distributing and combining like terms:
(15x - 57) / 2 + 18 = 4x
Step 4: Multiply every term in the equation by 2 to eliminate the fraction:
15x - 57 + 36 = 8x
Step 5: Combine like terms on the left side of the equation:
15x - 21 = 8x
Step 6: Subtract 8x from both sides to isolate the variable on one side of the equation:
15x - 8x - 21 = 0
Step 7: Simplify the equation:
7x - 21 = 0
Step 8: Add 21 to both sides to isolate the variable:
7x = 21
Step 9: Divide both sides by 7 to solve for x:
x = 3
Step 10: Substitute the value of x back into one of the original equations to find the value of y. Let's use the first equation:
5x - 19 = 2y
5(3) - 19 = 2y
15 - 19 = 2y
-4 = 2y
Step 11: Divide both sides by 2 to solve for y:
y = -2
So, the solution to the system of equations is x = 3 and y = -2.