Answer:
(1, 2)
Step-by-step explanation:
Substitution
Rearrange one of the two equations so that "y" is isolated, or by itself on one side of the equal sign.
3x + y = 5 => y = 5 - 3x
Substitute y for 5-3x in the other equation:
5x - 4y = -3
5x - 4(5 - 3x) = -3 Use the distributive property to expand
5x - 20 + 12x = -3 Collect like terms to simplify
17x - 20 = -3 Start isolating x
17x = -3 + 20
17x = 17 Divide both sides by 17
x = 1
Substitute x = 1 into one of the equations to find "y"
3x + y = 5
3(1) + y = 5
3 + y = 5 Isolate y by subtracting 3 from both sides
y = 2
Therefore the solution is (1, 2).
Elimination
Multiply one of the equations so that in each equation, there is a common variable and coefficient.
Multiply 3x + y = 5 by 4. It becomes 12x + 4y = 20.
Add each of the terms to add the equations together:
. 12x + 4y = 20
+ 5x - 4y = -3 If you add these two equations, the y variable is eliminated.
17x = 17 Divide both sides by 17 to isolate x
x = 1
Substitute x=1 into any of the equations.
3x + y = 5
3(1) + y = 5
3 + y = 5 Rearrange to isolate y
y = 2
Therefore the solutions is (1, 2).
