Solving two-variable linear equations given one value. Game on.

Solving two-variable linear equations given one value is a grade 9 math skill aligned to Common Core standard HSA.REI.B.3: solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 solving two-variable linear equations given one value problems our math games drill.

CCSS HSA.REI.B.310 questions in the bank
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Warm-upeasy

The equation 5a+3c=415a + 3c = 41 gives the total points scored from aa goals worth 55 points each and cc goals worth 33 points each. If a=4a = 4, what is the value of cc?

Substitute a=4a = 4: 5(4)+3c=415(4) + 3c = 41, so 20+3c=4120 + 3c = 41. Then 3c=213c = 21 and c=7c = 7.

Mid-gameeasy

The equation 2p+5q=392p + 5q = 39 gives the total weight, in pounds, of pp small boxes and qq large boxes. If q=3q = 3, what is the value of pp?

Substitute q=3q = 3: 2p+5(3)=392p + 5(3) = 39, so 2p+15=392p + 15 = 39. Then 2p=242p = 24 and p=12p = 12.

Mid-gameeasy

The equation 6h+4k=506h + 4k = 50 gives the total pay, in dollars, for hh hours at one rate and kk hours at another. If h=5h = 5, what is the value of kk?

Substitute h=5h = 5: 6(5)+4k=506(5) + 4k = 50, so 30+4k=5030 + 4k = 50. Then 4k=204k = 20 and k=5k = 5.

Mid-gameeasy

The equation 2t+3f=272t + 3f = 27 gives the total points from tt two-point conversions and ff field goals worth 33 points each. If t=6t = 6, what is the value of ff?

Substitute t=6t = 6: 2(6)+3f=272(6) + 3f = 27, so 12+3f=2712 + 3f = 27. Then 3f=153f = 15 and f=5f = 5.

Mid-gameeasy

The equation 4r+2s=304r + 2s = 30 gives the total length, in feet, of rr red ribbons and ss blue ribbons. If r=4r = 4, what is the value of ss?

Substitute r=4r = 4: 4(4)+2s=304(4) + 2s = 30, so 16+2s=3016 + 2s = 30. Then 2s=142s = 14 and s=7s = 7.

Mid-gameeasy

The equation 3u+4v=353u + 4v = 35 gives the total number of stamps in uu packs of 33 and vv packs of 44. If v=2v = 2, what is the value of uu?

Substitute v=2v = 2: 3u+4(2)=353u + 4(2) = 35, so 3u+8=353u + 8 = 35. Then 3u=273u = 27 and u=9u = 9.

Mid-gameeasy

The equation 5d+2e=445d + 2e = 44 gives the total distance, in miles, from dd trips of 55 miles and ee trips of 22 miles. If d=6d = 6, what is the value of ee?

Substitute d=6d = 6: 5(6)+2e=445(6) + 2e = 44, so 30+2e=4430 + 2e = 44. Then 2e=142e = 14 and e=7e = 7.

Buzzer beatermedium

The equation 8x+3y=558x + 3y = 55 gives the total cost, in dollars, of xx large posters and yy small posters. If y=5y = 5, what is the value of xx?

Substitute y=5y = 5: 8x+3(5)=558x + 3(5) = 55, so 8x+15=558x + 15 = 55. Then 8x=408x = 40 and x=5x = 5.

Tests that cover solving two-variable linear equations given one value:
PSAT 8/9SATSBACNC EOG/EOCNY State Math
More Grade 9 skills
Writing systems from contextLiteral equations (SAT)Linear systems by substitution (SAT)Literal quadratic equations (ACT)Linear system word problemsMonomial expression multiplication (SAT)Linear system expressionsPiecewise function composition (ACT)All Grade 9 practice →

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