How do you solve 3x – 2y = 26 and -7x + 3y = -49 using substitution?

1 Answer
Apr 15, 2018

x = 4
y =-7

Explanation:

Solve by simultaneous equations:

3x - 2y = 26
-7x+3y = -49

Rearrange 3x - 2y = 26 to make x the subject of the equation:

3x = 26 + 2y
x = (26 + 2y) / 3

Substitute the value of x into -7x+3y = -49:
-7*((26 + 2y) / 3) + 3y = -49
-7*(26/3 + (2y)/3) + 3y = -49

Multiply out the brackets:
-182/3 + -(14y)/3 + 3y = -49

Rearrange and place like terms together:
-(14y)/3 + 3y = -49 + 182/3

Simplify and solve for y:

-(5y)/3 = 35/3
-5y = 35/3 *3
-5y = 35
y = 35 / -5
y = -7

Use value of y to subsitute into any of the two original equations and solve for x:

3x - 2y = 26
3x - 2*(-7) = 26
3x + 14 = 26
3x = 26 - 14
3x = 12
x = 12/3
x = 4