System of Linear Equations
Question
Answer choices
- (3, 5)
- (3, 4)
- (0, 0)
- (4, 3)
- (4, 4)
B Correct answer: B) (3, 4)
Set up the problem carefully before computing. Substitution method: solve one equation for one variable, then plug it into the other equation.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
From the second equation, y = 7 - x. Substitute into the first: 2x + 2(7 - x) = 14. Expand: 2x + 14 - 2x = 14, so 0x = 0, giving x = 3. Then y = 7 - 3 = 4.
Why each wrong answer is wrong
- A) (3, 5): A common arithmetic or sign error leads to this value; carefully redo the calculation.
- C) (0, 0): A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) (4, 3): A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) (4, 4): A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Two unknowns require two equations. Substitute, eliminate, or graph — pick whichever is fastest. For ACT-level systems, substitution usually wins.
More Easy Intermediate Algebra
- Solving a Quadratic by FactoringSolve for x: x^2 - 5 x + 4 = 0.
- Function EvaluationIf f(x) = 3x^2 - 1, what is f(3)?
- System of Linear EquationsSolve the system: 2x + 2y = 14 and x + y = 7. Express your answer as (x, y).
- Exponent RulesSimplify (x^2)^2 · x^1.
- Solving a Quadratic by FactoringSolve for x: x^2 - 6 x + 5 = 0.